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-
¿Cómo usar?
- Ecuación diferencial:
- Ecuación -x*y+y'=-e^(-x^2)*y^3
- Ecuación y"+6y'+13y=0
- Ecuación x^2dy=y^2dx
- Ecuación x^2+y^2*y'=1
- Derivada de:
-
dy/dx
-
Expresiones idénticas
- dy/dx=- uno + uno /cos(x+y)
- dy dividir por dx es igual a menos 1 más 1 dividir por coseno de (x más y)
- dy dividir por dx es igual a menos uno más uno dividir por coseno de (x más y)
- dy/dx=-1+1/cosx+y
- dy dividir por dx=-1+1 dividir por cos(x+y)
-
Expresiones semejantes
- dy/dx=+1+1/cos(x+y)
- dy/dx=-1-1/cos(x+y)
- dy/dx=-1+1/cos(x-y)
-
Expresiones con funciones
- dy
- dy/dx=(y-3)/x
- dy/dx=y/(2x)
- dy/dx=(x-y)/(x+y)
- dy/dx=-x/y
- dy/dx=(x-y)/x
- dx
- dx*(x/sqrt(x^2+y^2)+y)+dy*(x+y/sqrt(x^2+y^2))=0
- dx*(x^3*y^2+x*y-cos(x))+dy*(x^4*y/2+x^2/2-2)=0
- dx*(4-y^2/x^2)+2*dy*y/x=0
- dx*(2*x*y+3*x^(2*y)+y^3)+dy*(x^2+y^2)=0
- dx*(2*x*y^2+y+cos(x))+dy*(2^y*log(2)+2*x^2*y+x)=0
- Coseno cos
- cos^2×5xdy=sin^2×5ydx
- cos(x)+cos(y)=7*dy*y/dx
- cos(5x^2-3)xdx
- cos(x)*dx-3y*dy=0
- cos(3*x)^2*y''=1
Ecuación diferencial dy/dx=-1+1/cos(x+y)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d 1 --(y(x)) = -1 + ------------- dx cos(x + y(x))
$$\frac{d}{d x} y{\left(x \right)} = -1 + \frac{1}{\cos{\left(x + y{\left(x \right)} \right)}}$$
y' = -1 + 1/cos(x + y)
Solución detallada
Tenemos la ecuación:
$$\frac{d}{d x} y{\left(x \right)} + 1 - \frac{1}{\cos{\left(x + y{\left(x \right)} \right)}} = 0$$
Sustituimos
$$u{\left(x \right)} = x + y{\left(x \right)}$$
y porque
$$\frac{d}{d x} y{\left(x \right)} + 1 = \frac{d}{d x} u{\left(x \right)}$$
entonces
$$\frac{d}{d x} y{\left(x \right)} = \frac{d}{d x} u{\left(x \right)} - 1$$
sustituimos
$$\frac{d}{d x} \left(- x + u{\left(x \right)}\right) + 1 - \frac{1}{\cos{\left(u{\left(x \right)} \right)}} = 0$$
o
$$\frac{d}{d x} u{\left(x \right)} - \frac{1}{\cos{\left(u{\left(x \right)} \right)}} = 0$$
Esta ecuación diferencial tiene la forma:
donde
$$\operatorname{f_{1}}{\left(x \right)} = 1$$
$$\operatorname{g_{1}}{\left(u \right)} = 1$$
$$\operatorname{f_{2}}{\left(x \right)} = 1$$
$$\operatorname{g_{2}}{\left(u \right)} = \frac{1}{\cos{\left(u{\left(x \right)} \right)}}$$
Pasemos la ecuación a la forma:
Dividamos ambos miembros de la ecuación en g2(u)
$$\frac{1}{\cos{\left(u{\left(x \right)} \right)}}$$
obtendremos
$$\cos{\left(u{\left(x \right)} \right)} \frac{d}{d x} u{\left(x \right)} = 1$$
Con esto hemos separado las variables x y u.
Ahora multipliquemos las dos partes de la ecuación por dx,
entonces la ecuación será así
$$dx \cos{\left(u{\left(x \right)} \right)} \frac{d}{d x} u{\left(x \right)} = dx$$
o
$$du \cos{\left(u{\left(x \right)} \right)} = dx$$
Tomemos la integral de las dos partes de la ecuación:
- de la parte izquierda la integral por u,
- de la parte derecha la integral por x.
$$\int \cos{\left(u \right)}\, du = \int 1\, dx$$
Tomemos estas integrales
$$\sin{\left(u \right)} = Const + x$$
Hemos recibido una ecuación ordinaria con la incógnica u.
(Const - es una constante)
La solución:
$$\operatorname{u_{1}} = u{\left(x \right)} = \pi - \operatorname{asin}{\left(C_{1} + x \right)}$$
$$\operatorname{u_{2}} = u{\left(x \right)} = \operatorname{asin}{\left(C_{1} + x \right)}$$
hacemos cambio inverso
$$y{\left(x \right)} = - x + u{\left(x \right)}$$
$$y1 = y(x) = - x - \operatorname{asin}{\left(C_{1} + x \right)} + \pi$$
$$y2 = y(x) = - x + \operatorname{asin}{\left(C_{1} + x \right)}$$
$$\frac{d}{d x} y{\left(x \right)} + 1 - \frac{1}{\cos{\left(x + y{\left(x \right)} \right)}} = 0$$
Sustituimos
$$u{\left(x \right)} = x + y{\left(x \right)}$$
y porque
$$\frac{d}{d x} y{\left(x \right)} + 1 = \frac{d}{d x} u{\left(x \right)}$$
entonces
$$\frac{d}{d x} y{\left(x \right)} = \frac{d}{d x} u{\left(x \right)} - 1$$
sustituimos
$$\frac{d}{d x} \left(- x + u{\left(x \right)}\right) + 1 - \frac{1}{\cos{\left(u{\left(x \right)} \right)}} = 0$$
o
$$\frac{d}{d x} u{\left(x \right)} - \frac{1}{\cos{\left(u{\left(x \right)} \right)}} = 0$$
Esta ecuación diferencial tiene la forma:
f1(x)*g1(u)*u' = f2(x)*g2(u),
donde
$$\operatorname{f_{1}}{\left(x \right)} = 1$$
$$\operatorname{g_{1}}{\left(u \right)} = 1$$
$$\operatorname{f_{2}}{\left(x \right)} = 1$$
$$\operatorname{g_{2}}{\left(u \right)} = \frac{1}{\cos{\left(u{\left(x \right)} \right)}}$$
Pasemos la ecuación a la forma:
g1(u)/g2(u)*u'= f2(x)/f1(x).
Dividamos ambos miembros de la ecuación en g2(u)
$$\frac{1}{\cos{\left(u{\left(x \right)} \right)}}$$
obtendremos
$$\cos{\left(u{\left(x \right)} \right)} \frac{d}{d x} u{\left(x \right)} = 1$$
Con esto hemos separado las variables x y u.
Ahora multipliquemos las dos partes de la ecuación por dx,
entonces la ecuación será así
$$dx \cos{\left(u{\left(x \right)} \right)} \frac{d}{d x} u{\left(x \right)} = dx$$
o
$$du \cos{\left(u{\left(x \right)} \right)} = dx$$
Tomemos la integral de las dos partes de la ecuación:
- de la parte izquierda la integral por u,
- de la parte derecha la integral por x.
$$\int \cos{\left(u \right)}\, du = \int 1\, dx$$
Tomemos estas integrales
$$\sin{\left(u \right)} = Const + x$$
Hemos recibido una ecuación ordinaria con la incógnica u.
(Const - es una constante)
La solución:
$$\operatorname{u_{1}} = u{\left(x \right)} = \pi - \operatorname{asin}{\left(C_{1} + x \right)}$$
$$\operatorname{u_{2}} = u{\left(x \right)} = \operatorname{asin}{\left(C_{1} + x \right)}$$
hacemos cambio inverso
$$y{\left(x \right)} = - x + u{\left(x \right)}$$
$$y1 = y(x) = - x - \operatorname{asin}{\left(C_{1} + x \right)} + \pi$$
$$y2 = y(x) = - x + \operatorname{asin}{\left(C_{1} + x \right)}$$
Respuesta
[src]
/ / / 2 / 1 \ \ \ / 2 / 1 \ \ \
| | | 2 2 2*sin (C1)*|-1 + -------| | | | 2 2 2*sin (C1)*|-1 + -------| | |
| | | sin (C1) 2*sin (C1) \ cos(C1)/ | | | sin (C1) 2*sin (C1) \ cos(C1)/ | |
| 2 / 1 \ / 2 / 1 \ / 2 / 1 \\ / 2 / 1 \\ \ | 2 / 1 \ / 2 / 1 \ / 2 / 1 \\ / 2 / 1 \\ \ | 1 + -------- + ---------- + ------------------------- / 2 / 1 \\ 2 / 1 \| / 2 / 1 \\ / 2 / 1 \\ | | 1 + -------- + ---------- + ------------------------- / 2 / 1 \\ 2 / 1 \| / 2 / 1 \\ / 2 / 1 \\ | / 2 / 1 \ / 2 / 1 \ \ \
| 2 2 2*sin (C1)*|-1 + -------| | 2 2 2*sin (C1)*|-1 + -------| | 2 2 2*sin (C1)*|-1 + -------|| | 2 2 3*sin (C1)*|-1 + -------|| | | 2 2 2*sin (C1)*|-1 + -------| | 2 2 2*sin (C1)*|-1 + -------| | 2 2 2*sin (C1)*|-1 + -------|| | 2 2 3*sin (C1)*|-1 + -------|| | | 2 cos(C1) cos(C1) | 2 2 3*sin (C1)*|-1 + -------|| 2 2 6*sin (C1)*|-1 + -------|| | 2 2 2*sin (C1)*|-1 + -------|| | 2 2 3*sin (C1)*|-1 + -------|| | | 2 cos(C1) cos(C1) | 2 2 3*sin (C1)*|-1 + -------|| 2 2 6*sin (C1)*|-1 + -------|| | 2 2 2*sin (C1)*|-1 + -------|| | 2 2 3*sin (C1)*|-1 + -------|| | | 2 2 2*sin (C1)*|-1 + -------| | 2 2 2*sin (C1)*|-1 + -------| | |
| sin (C1) 2*sin (C1) \ cos(C1)/ | sin (C1) 2*sin (C1) \ cos(C1)/ 2 | sin (C1) 2*sin (C1) \ cos(C1)/| 2 | 3*sin (C1) 3*sin (C1) \ cos(C1)/| | | sin (C1) 2*sin (C1) \ cos(C1)/ | sin (C1) 2*sin (C1) \ cos(C1)/ 2 | sin (C1) 2*sin (C1) \ cos(C1)/| 2 | 3*sin (C1) 3*sin (C1) \ cos(C1)/| | 2 | cos (C1) / 1 \ | 3*sin (C1) 3*sin (C1) \ cos(C1)/| 6*sin (C1) 6*sin (C1) \ cos(C1)/| 2 | sin (C1) 2*sin (C1) \ cos(C1)/| 2 | 3*sin (C1) 3*sin (C1) \ cos(C1)/| | 2 | cos (C1) / 1 \ | 3*sin (C1) 3*sin (C1) \ cos(C1)/| 6*sin (C1) 6*sin (C1) \ cos(C1)/| 2 | sin (C1) 2*sin (C1) \ cos(C1)/| 2 | 3*sin (C1) 3*sin (C1) \ cos(C1)/| | | sin (C1) 2*sin (C1) \ cos(C1)/ | sin (C1) 2*sin (C1) \ cos(C1)/ | |
/ / 2 / 1 \\ 2 / 1 \\ | 1 + -------- + ---------- + ------------------------- | 1 + -------- + ---------- + ------------------------- / 4 / 1 \ 2 / 1 \\ 2*sin (C1)*|1 + -------- + ---------- + -------------------------| 4*sin (C1)*|4 + ---------- + ---------- + -------------------------| 4 / 1 \ 2 / 1 \| | 1 + -------- + ---------- + ------------------------- | 1 + -------- + ---------- + ------------------------- / 4 / 1 \ 2 / 1 \\ 2*sin (C1)*|1 + -------- + ---------- + -------------------------| 4*sin (C1)*|4 + ---------- + ---------- + -------------------------| 4 / 1 \ 2 / 1 \| / 4 / 1 \ 2 / 1 \\ sin (C1)*|8 + ----------------------------------------------------- + 2*|-1 + -------|*|4 + ---------- + ---------- + -------------------------| + ---------- + ---------- + -------------------------| 2*sin (C1)*|1 + -------- + ---------- + -------------------------| 4*sin (C1)*|4 + ---------- + ---------- + -------------------------| 4 / 1 \ 2 / 1 \| / 4 / 1 \ 2 / 1 \\ sin (C1)*|8 + ----------------------------------------------------- + 2*|-1 + -------|*|4 + ---------- + ---------- + -------------------------| + ---------- + ---------- + -------------------------| 2*sin (C1)*|1 + -------- + ---------- + -------------------------| 4*sin (C1)*|4 + ---------- + ---------- + -------------------------| 4 / 1 \ 2 / 1 \| | 1 + -------- + ---------- + ------------------------- | 1 + -------- + ---------- + ------------------------- / 2 / 1 \\ 2 / 1 \| / 2 / 1 \\ 2 / 1 \|
| 2 | 2 2 2*sin (C1)*|-1 + -------|| 2 2*sin (C1)*|-1 + -------|| | 2 cos(C1) cos(C1) | 2 cos(C1) cos(C1) | 4 2 2 4 6*sin (C1)*|-1 + -------| 7*sin (C1)*|-1 + -------|| 4 2 2 4 | 2 cos(C1) cos(C1) | | cos(C1) 2 cos(C1) | 24*sin (C1)*|-1 + -------| 28*sin (C1)*|-1 + -------|| | 2 cos(C1) cos(C1) | 2 cos(C1) cos(C1) | 4 2 2 4 6*sin (C1)*|-1 + -------| 7*sin (C1)*|-1 + -------|| 4 2 2 4 | 2 cos(C1) cos(C1) | | cos(C1) 2 cos(C1) | 24*sin (C1)*|-1 + -------| 28*sin (C1)*|-1 + -------|| | 4 2 2 4 6*sin (C1)*|-1 + -------| 7*sin (C1)*|-1 + -------|| 4 2 2 4 | cos(C1) \ cos(C1)/ | cos(C1) 2 cos(C1) | cos(C1) 2 cos(C1) | | 2 cos(C1) cos(C1) | | cos(C1) 2 cos(C1) | 24*sin (C1)*|-1 + -------| 28*sin (C1)*|-1 + -------|| | 4 2 2 4 6*sin (C1)*|-1 + -------| 7*sin (C1)*|-1 + -------|| 4 2 2 4 | cos(C1) \ cos(C1)/ | cos(C1) 2 cos(C1) | cos(C1) 2 cos(C1) | | 2 cos(C1) cos(C1) | | cos(C1) 2 cos(C1) | 24*sin (C1)*|-1 + -------| 28*sin (C1)*|-1 + -------|| | 2 cos(C1) cos(C1) | 2 cos(C1) cos(C1) | 2 2 3*sin (C1)*|-1 + -------|| 2 2 6*sin (C1)*|-1 + -------|| | 2 2 3*sin (C1)*|-1 + -------|| 2 2 6*sin (C1)*|-1 + -------||
3 | sin (C1) / 1 \ | sin (C1) 2*sin (C1) \ cos(C1)/| 2*sin (C1) \ cos(C1)/| 5 | cos (C1) / 1 \ | cos (C1) / 1 \ | 6*sin (C1) 7*sin (C1) 8*sin (C1) 9*sin (C1) \ cos(C1)/ \ cos(C1)/| 24*sin (C1) 28*sin (C1) 32*sin (C1) 36*sin (C1) \ cos (C1) / \ cos (C1) / \ cos(C1)/ \ cos(C1)/| / 1 \ | cos (C1) / 1 \ | cos (C1) / 1 \ | 6*sin (C1) 7*sin (C1) 8*sin (C1) 9*sin (C1) \ cos(C1)/ \ cos(C1)/| 24*sin (C1) 28*sin (C1) 32*sin (C1) 36*sin (C1) \ cos (C1) / \ cos (C1) / \ cos(C1)/ \ cos(C1)/| / 1 \ | 6*sin (C1) 7*sin (C1) 8*sin (C1) 9*sin (C1) \ cos(C1)/ \ cos(C1)/| 24*sin (C1) 28*sin (C1) 32*sin (C1) 36*sin (C1) \ \ cos (C1) / cos (C1) / \ cos (C1) / \ cos (C1) / \ cos(C1)/ \ cos(C1)/| / 1 \ | 6*sin (C1) 7*sin (C1) 8*sin (C1) 9*sin (C1) \ cos(C1)/ \ cos(C1)/| 24*sin (C1) 28*sin (C1) 32*sin (C1) 36*sin (C1) \ \ cos (C1) / cos (C1) / \ cos (C1) / \ cos (C1) / \ cos(C1)/ \ cos(C1)/| 4 | cos (C1) / 1 \ | cos (C1) / 1 \ | 3*sin (C1) 3*sin (C1) \ cos(C1)/| 6*sin (C1) 6*sin (C1) \ cos(C1)/| / 1 \ | 3*sin (C1) 3*sin (C1) \ cos(C1)/| 6*sin (C1) 6*sin (C1) \ cos(C1)/|
x *|1 + -------- + |-1 + -------|*|1 + -------- + ---------- + -------------------------| + ---------- + -------------------------| x *|8 + ----------------------------------------------------- + |-1 + -------|*|8 + ----------------------------------------------------- + 4*|-1 + -------|*|2 + ---------- + ---------- + ---------- + ---------- + ------------------------- + -------------------------| + ----------- + ----------- + ----------- + ----------- + ------------------------------------------------------------------ + -------------------------------------------------------------------- + -------------------------- + --------------------------| + |-1 + -------|*|8 + ----------------------------------------------------- + |-1 + -------|*|8 + ----------------------------------------------------- + 4*|-1 + -------|*|2 + ---------- + ---------- + ---------- + ---------- + ------------------------- + -------------------------| + ----------- + ----------- + ----------- + ----------- + ------------------------------------------------------------------ + -------------------------------------------------------------------- + -------------------------- + --------------------------| + 4*|-1 + -------|*|2 + ---------- + ---------- + ---------- + ---------- + ------------------------- + -------------------------| + ----------- + ----------- + ----------- + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------------------------------- + -------------------------- + --------------------------| + 4*|-1 + -------|*|2 + ---------- + ---------- + ---------- + ---------- + ------------------------- + -------------------------| + ----------- + ----------- + ----------- + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------------------------------- + -------------------------- + --------------------------| x *|8 + ----------------------------------------------------- + |-1 + -------|*|8 + ----------------------------------------------------- + 2*|-1 + -------|*|4 + ---------- + ---------- + -------------------------| + ---------- + ---------- + -------------------------| + 2*|-1 + -------|*|4 + ---------- + ---------- + -------------------------| + ---------- + ---------- + -------------------------|*sin(C1)
2 | 2 \ cos(C1)/ | 2 cos(C1) cos(C1) | cos(C1) cos(C1) | | cos(C1) \ cos(C1)/ | cos(C1) \ cos(C1)/ | 3 cos(C1) 2 4 3 cos(C1) | 3 cos(C1) 2 4 3 3 3 cos(C1) | \ cos(C1)/ | cos(C1) \ cos(C1)/ | cos(C1) \ cos(C1)/ | 3 cos(C1) 2 4 3 cos(C1) | 3 cos(C1) 2 4 3 3 3 cos(C1) | \ cos(C1)/ | 3 cos(C1) 2 4 3 cos(C1) | 3 cos(C1) 2 4 3 3 3 3 cos(C1) | \ cos(C1)/ | 3 cos(C1) 2 4 3 cos(C1) | 3 cos(C1) 2 4 3 3 3 3 cos(C1) | | cos(C1) \ cos(C1)/ | cos(C1) \ cos(C1)/ | cos(C1) 2 cos(C1) | cos(C1) 2 cos(C1) | \ cos(C1)/ | cos(C1) 2 cos(C1) | cos(C1) 2 cos(C1) |
/ 1 \ x *sin(C1) \ cos (C1) \ cos (C1) / / \ \ \ cos (C1) cos (C1) cos (C1) cos (C1) / cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) / \ \ \ cos (C1) cos (C1) cos (C1) cos (C1) / cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) / \ cos (C1) cos (C1) cos (C1) cos (C1) / cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) / \ cos (C1) cos (C1) cos (C1) cos (C1) / cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) cos (C1) / \ \ \ cos (C1) / cos (C1) / \ cos (C1) / cos (C1) / / 6\
y(x) = C1 + x*|-1 + -------| + ---------- + ----------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
\ cos(C1)/ 3 2 2 3
2*cos (C1) 6*cos (C1) 120*cos (C1) 24*cos (C1)
$$y{\left(x \right)} = x \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) + \frac{x^{2} \sin{\left(C_{1} \right)}}{2 \cos^{3}{\left(C_{1} \right)}} + \frac{x^{3} \left(\left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right) + \frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right)}{6 \cos^{2}{\left(C_{1} \right)}} + \frac{x^{4} \left(2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) + \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) + \frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) + \frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) \sin{\left(C_{1} \right)}}{24 \cos^{3}{\left(C_{1} \right)}} + \frac{x^{5} \left(4 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{7 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{9 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{7 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{8 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 2\right) + \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(4 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{7 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{9 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{7 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{8 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 2\right) + \frac{24 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{28 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \left(\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{4 \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{24 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{36 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{28 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{32 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) + \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(4 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{7 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{9 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{7 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{8 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 2\right) + \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(4 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{7 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{9 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{7 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{8 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 2\right) + \frac{24 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{28 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \left(\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{4 \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{24 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{36 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{28 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{32 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) + \frac{24 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{28 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \left(\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{4 \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\left(2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) + \frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{24 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{36 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{28 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{32 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) + \frac{24 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{28 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \left(\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{4 \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{\left(2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \left(\frac{3 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{3 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 4\right) + \frac{6 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\frac{2 \left(-1 + \frac{1}{\cos{\left(C_{1} \right)}}\right) \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{2 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{\sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 1}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{6 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right) \sin^{2}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{24 \sin^{4}{\left(C_{1} \right)}}{\cos^{3}{\left(C_{1} \right)}} + \frac{36 \sin^{4}{\left(C_{1} \right)}}{\cos^{4}{\left(C_{1} \right)}} + \frac{28 \sin^{2}{\left(C_{1} \right)}}{\cos{\left(C_{1} \right)}} + \frac{32 \sin^{2}{\left(C_{1} \right)}}{\cos^{2}{\left(C_{1} \right)}} + 8\right)}{120 \cos^{2}{\left(C_{1} \right)}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -2.169463124154396)
(-5.555555555555555, 6.9520529151772e-310)
(-3.333333333333333, 6.9518346485953e-310)
(-1.1111111111111107, 6.9518346486016e-310)
(1.1111111111111107, 6.95183464860793e-310)
(3.333333333333334, 6.95183464861425e-310)
(5.555555555555557, 6.95183464918974e-310)
(7.777777777777779, 6.9520529151772e-310)
(10.0, 6.9518346493257e-310)
(10.0, 6.9518346493257e-310)