Sr Examen
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- Ecuaciones diferenciales lineales no homogéneas de primer orden paso a paso
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- Ecuaciones diferenciales ordinarias de primer orden paso a paso
- Convergencia de la serie – estudio en línea
- Solución del problema de Cauchy en línea
-
¿Cómo usar?
- Ecuación diferencial:
- Ecuación dy/dx=2+√(y-2x+3)
- Ecuación y'''''-3y''''+3y'''-y''=0
- Ecuación (1-x)dy-ydx=0
- Ecuación y''-2y'+y=2e^x
- Derivada de:
-
dy/dx
-
Expresiones idénticas
- dy/dx= dos +√(y-2x+ tres)
- dy dividir por dx es igual a 2 más √(y menos 2x más 3)
- dy dividir por dx es igual a dos más √(y menos 2x más tres)
- dy/dx=2+√y-2x+3
- dy dividir por dx=2+√(y-2x+3)
-
Expresiones semejantes
- dy/dx=2+√(y-2x-3)
- dy/dx=2-√(y-2x+3)
- dy/dx=2+√(y+2x+3)
- (dy)/(dx)=(3x^2+4x+2)/(2(y-1))
-
Expresiones con funciones
- dy
- dy/dx=(y/x)+(x^2/y^2)+(1)
- dy/dt+20y=24y=6/5-6/5e-20
- dy/dx=(1-x-y)/(x+y)
- dy/dx=((2y+3)/(4x+5))^2
- dy/dx=(y^2-1)/(x^2-1)
- dx
- dx-x^2dy=0
- dx/dt=2x+y
- dx+(x/y-seny)dy=0
- dx/dt=x+y
- dx/dy-2y=e^3x+10e^2x
Ecuación diferencial dy/dx=2+√(y-2x+3)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d ________________ --(y(x)) = 2 + \/ 3 - 2*x + y(x) dx
$$\frac{d}{d x} y{\left(x \right)} = \sqrt{- 2 x + y{\left(x \right)} + 3} + 2$$
y' = sqrt(-2*x + y + 3) + 2
Solución detallada
Tenemos la ecuación:
$$- \sqrt{- 2 x + y{\left(x \right)} + 3} + \frac{d}{d x} y{\left(x \right)} - 2 = 0$$
Sustituimos
$$u{\left(x \right)} = - 2 x + y{\left(x \right)} + 3$$
y porque
$$\frac{d}{d x} y{\left(x \right)} - 2 = \frac{d}{d x} u{\left(x \right)}$$
entonces
$$\frac{d}{d x} y{\left(x \right)} = \frac{d}{d x} u{\left(x \right)} + 2$$
sustituimos
$$- \sqrt{u{\left(x \right)}} + \frac{d}{d x} \left(2 x + u{\left(x \right)} - 3\right) - 2 = 0$$
o
$$- \sqrt{u{\left(x \right)}} + \frac{d}{d x} u{\left(x \right)} = 0$$
Esta ecuación diferencial tiene la forma:
donde
$$\operatorname{f_{1}}{\left(x \right)} = 1$$
$$\operatorname{g_{1}}{\left(u \right)} = 1$$
$$\operatorname{f_{2}}{\left(x \right)} = 1$$
$$\operatorname{g_{2}}{\left(u \right)} = \sqrt{u{\left(x \right)}}$$
Pasemos la ecuación a la forma:
Dividamos ambos miembros de la ecuación en g2(u)
$$\sqrt{u{\left(x \right)}}$$
obtendremos
$$\frac{\frac{d}{d x} u{\left(x \right)}}{\sqrt{u{\left(x \right)}}} = 1$$
Con esto hemos separado las variables x y u.
Ahora multipliquemos las dos partes de la ecuación por dx,
entonces la ecuación será así
$$\frac{dx \frac{d}{d x} u{\left(x \right)}}{\sqrt{u{\left(x \right)}}} = dx$$
o
$$\frac{du}{\sqrt{u{\left(x \right)}}} = dx$$
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.
$$\int \frac{1}{\sqrt{u}}\, du = \int 1\, dx$$
Tomemos estas integrales
$$2 \sqrt{u} = Const + x$$
Hemos recibido una ecuación ordinaria con la incógnica u.
(Const - es una constante)
La solución:
$$\operatorname{u_{1}} = u{\left(x \right)} = \frac{C_{1}^{2}}{4} + \frac{C_{1} x}{2} + \frac{x^{2}}{4}$$
hacemos cambio inverso
$$y{\left(x \right)} = 2 x + u{\left(x \right)} - 3$$
$$y1 = y(x) = \frac{C_{1}^{2}}{4} + \frac{C_{1} x}{2} + \frac{x^{2}}{4} + 2 x - 3$$
$$- \sqrt{- 2 x + y{\left(x \right)} + 3} + \frac{d}{d x} y{\left(x \right)} - 2 = 0$$
Sustituimos
$$u{\left(x \right)} = - 2 x + y{\left(x \right)} + 3$$
y porque
$$\frac{d}{d x} y{\left(x \right)} - 2 = \frac{d}{d x} u{\left(x \right)}$$
entonces
$$\frac{d}{d x} y{\left(x \right)} = \frac{d}{d x} u{\left(x \right)} + 2$$
sustituimos
$$- \sqrt{u{\left(x \right)}} + \frac{d}{d x} \left(2 x + u{\left(x \right)} - 3\right) - 2 = 0$$
o
$$- \sqrt{u{\left(x \right)}} + \frac{d}{d x} u{\left(x \right)} = 0$$
Esta ecuación diferencial tiene la forma:
f1(x)*g1(u)*u' = f2(x)*g2(u),
donde
$$\operatorname{f_{1}}{\left(x \right)} = 1$$
$$\operatorname{g_{1}}{\left(u \right)} = 1$$
$$\operatorname{f_{2}}{\left(x \right)} = 1$$
$$\operatorname{g_{2}}{\left(u \right)} = \sqrt{u{\left(x \right)}}$$
Pasemos la ecuación a la forma:
g1(u)/g2(u)*u'= f2(x)/f1(x).
Dividamos ambos miembros de la ecuación en g2(u)
$$\sqrt{u{\left(x \right)}}$$
obtendremos
$$\frac{\frac{d}{d x} u{\left(x \right)}}{\sqrt{u{\left(x \right)}}} = 1$$
Con esto hemos separado las variables x y u.
Ahora multipliquemos las dos partes de la ecuación por dx,
entonces la ecuación será así
$$\frac{dx \frac{d}{d x} u{\left(x \right)}}{\sqrt{u{\left(x \right)}}} = dx$$
o
$$\frac{du}{\sqrt{u{\left(x \right)}}} = dx$$
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.
$$\int \frac{1}{\sqrt{u}}\, du = \int 1\, dx$$
Tomemos estas integrales
$$2 \sqrt{u} = Const + x$$
Hemos recibido una ecuación ordinaria con la incógnica u.
(Const - es una constante)
La solución:
$$\operatorname{u_{1}} = u{\left(x \right)} = \frac{C_{1}^{2}}{4} + \frac{C_{1} x}{2} + \frac{x^{2}}{4}$$
hacemos cambio inverso
$$y{\left(x \right)} = 2 x + u{\left(x \right)} - 3$$
$$y1 = y(x) = \frac{C_{1}^{2}}{4} + \frac{C_{1} x}{2} + \frac{x^{2}}{4} + 2 x - 3$$
Respuesta
[src]
/ / ________ \ \
| | 1 2 2 + \/ 3 + C1 | |
| | ------ + ----------- - -------------- | |
/ / ________ \ \ | ________ / ________ / ________\ / ________\ \ | 3 + C1 3/2 3/2 / ________\ / ________\ / ________ / ________\ \ / ________\ / ________\ / ________\ | |
| | 1 2 2 + \/ 3 + C1 | | | 1 2 2 + \/ 3 + C1 | 1 2 2 + \/ 3 + C1 | 1 2 2 + \/ 3 + C1 | | 1 2 2 + \/ 3 + C1 | | | 6 12 (3 + C1) (3 + C1) 6*\2 + \/ 3 + C1 / / ________\ | 1 2 2 + \/ 3 + C1 | | 1 2 2 + \/ 3 + C1 | 1 2 2 + \/ 3 + C1 | | | 1 2 2 + \/ 3 + C1 | | 1 2 2 + \/ 3 + C1 | | 1 2 2 + \/ 3 + C1 | | |
| | ------ + ----------- - -------------- | | | ------ + ----------- - -------------- | ------ + ----------- - -------------- 3*|- --------- - ----------- + --------------| 3*|--------- + ----------- - --------------| | | --------- + ----------- + ------------------------------------- - ------------------ + 3*\2 + \/ 3 + C1 /*|- --------- - ----------- + --------------| | ------ + ----------- - -------------- 6*|- --------- - ----------- + --------------| | 6*|- --------- - ----------- + --------------| 2*|------ + ----------- - --------------| 6*|--------- + ----------- - --------------| | |
/ / ________\\ | ________ | 3 + C1 3/2 3/2 / ________\ / ________\| / ________\| | / ________\ ________ 3 + C1 3/2 3/2 / ________\ / ________\ | 3 + C1 3/2 3/2 / ________\ | 2 5/2 5/2 | | 2 5/2 5/2 | / ________\| | 2 5/2 ________ 5/2 | 2 5/2 5/2 | | 3 + C1 3/2 3/2 | 2 5/2 5/2 | / ________\ / ________\| / ________\ | 2 5/2 5/2 | |3 + C1 3/2 3/2 | | 2 5/2 5/2 | / ________\| / ________\|
| / ________\ | 1 2 2 + \/ 3 + C1 || | 1 2 2 + \/ 3 + C1 / ________\ | 6 12 (3 + C1) (3 + C1) 6*\2 + \/ 3 + C1 / / ________\ | 1 2 2 + \/ 3 + C1 || / ________\ | 1 2 2 + \/ 3 + C1 || | | 1 2 2 + \/ 3 + C1 | 1 2 2 + \/ 3 + C1 6 12 (3 + C1) (3 + C1) 6*\2 + \/ 3 + C1 / / ________\ | 1 2 2 + \/ 3 + C1 | / ________\ | 30 60 (3 + C1) (3 + C1) 30*\2 + \/ 3 + C1 / \ (3 + C1) (3 + C1) (3 + C1) / \(3 + C1) (3 + C1) (3 + C1) / / ________\ | 1 2 2 + \/ 3 + C1 || / ________\ | 60 120 (3 + C1) (3 + C1) \/ 3 + C1 (3 + C1) \ (3 + C1) (3 + C1) (3 + C1) / / ________\ | 60 30 (3 + C1) (3 + C1) \ (3 + C1) (3 + C1) (3 + C1) / / ________\ | 1 2 2 + \/ 3 + C1 | 30*\2 + \/ 3 + C1 /| 60*\2 + \/ 3 + C1 / \ (3 + C1) (3 + C1) (3 + C1) / \ (3 + C1) (3 + C1) / \(3 + C1) (3 + C1) (3 + C1) / / ________\ | 1 2 2 + \/ 3 + C1 || / ________\ | 1 2 2 + \/ 3 + C1 ||
| \2 + \/ 3 + C1 /*|------ + ----------- - --------------|| | ------ + ----------- - -------------- \2 + \/ 3 + C1 /*|--------- + ----------- + ------------------------------------- - ------------------ + 3*\2 + \/ 3 + C1 /*|- --------- - ----------- + --------------|| 3*\2 + \/ 3 + C1 /*|--------- + ----------- - --------------|| | 3*|--------- + ----------- - --------------| ------ + ----------- - -------------- --------- + ----------- + ------------------------------------- - ------------------ + 3*\2 + \/ 3 + C1 /*|- --------- - ----------- + --------------| \2 + \/ 3 + C1 /*|--------- + ----------- + ------------------------------------- - ------------------- - ---------------------------------------------- + -------------------------------------------- + 15*\2 + \/ 3 + C1 /*|- --------- - ----------- + --------------|| \2 + \/ 3 + C1 /*|--------- + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------ + \2 + \/ 3 + C1 /*|- ----------- - --------- - ------------------------------------- + ---------------------------------------------- + 15*\2 + \/ 3 + C1 /*|--------- + ----------- - --------------| + -------------------| - ------------------- - ---------------------------------------------- + ----------------------------------------- + -------------------------------------------- + 30*\2 + \/ 3 + C1 /*|- --------- - ----------- + --------------|| 15*\2 + \/ 3 + C1 /*|--------- + ----------- - --------------||
| ________ |3 + C1 3/2 3/2 || | 3 + C1 3/2 3/2 | 2 5/2 ________ 5/2 | 2 5/2 5/2 || / ________\ | 2 5/2 5/2 || | | 2 5/2 5/2 | 3 + C1 3/2 3/2 2 5/2 ________ 5/2 | 2 5/2 5/2 | | 3 7/2 3/2 7/2 ________ ________ | 3 7/2 7/2 || | 3 7/2 ________ | 7/2 3 3/2 ________ | 3 7/2 7/2 | 7/2 | 7/2 ________ 3/2 ________ | 3 7/2 7/2 || / ________\ | 3 7/2 7/2 ||
3 | 1 1 2 + \/ 3 + C1 \ (3 + C1) (3 + C1) /| 4 | 3 3 (3 + C1) (3 + C1) \(3 + C1) (3 + C1) \/ 3 + C1 (3 + C1) \ (3 + C1) (3 + C1) (3 + C1) // 3*\2 + \/ 3 + C1 / \(3 + C1) (3 + C1) (3 + C1) /| 5 | 15 15 \(3 + C1) (3 + C1) (3 + C1) / (3 + C1) (3 + C1) (3 + C1) (3 + C1) \/ 3 + C1 (3 + C1) \ (3 + C1) (3 + C1) (3 + C1) / \(3 + C1) (3 + C1) (3 + C1) (3 + C1) \/ 3 + C1 \/ 3 + C1 \ (3 + C1) (3 + C1) (3 + C1) // \(3 + C1) (3 + C1) \/ 3 + C1 \ (3 + C1) (3 + C1) (3 + C1) \/ 3 + C1 \(3 + C1) (3 + C1) (3 + C1) / (3 + C1) / (3 + C1) \/ 3 + C1 (3 + C1) \/ 3 + C1 \ (3 + C1) (3 + C1) (3 + C1) // 15*\2 + \/ 3 + C1 / \(3 + C1) (3 + C1) (3 + C1) /|
x *|- ----------- - ---------- + -------------- + --------------------------------------------------------| x *|- ----------- - ----------- - ------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------ + -------------------------------------------------------------| x *|- ----------- - ----------- - -------------------------------------------- - ------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------- + --------------------------------------------------------------|
2 | 3/2 2*(3 + C1) 3/2 4 | | 5/2 2 ________ 8 5/2 4 | | 7/2 3 ________ 3/2 ________ 8 16 7/2 4 |
x / ________\ \ (3 + C1) 2*(3 + C1) / \ (3 + C1) 2*(3 + C1) 4*\/ 3 + C1 2*(3 + C1) / \ (3 + C1) 2*(3 + C1) 2*\/ 3 + C1 4*(3 + C1) 8*\/ 3 + C1 2*(3 + C1) / / 6\
y(x) = C1 + -- + x*\2 + \/ 3 + C1 / + ----------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
4 6 24 120
$$y{\left(x \right)} = x \left(\sqrt{C_{1} + 3} + 2\right) + \frac{x^{2}}{4} + \frac{x^{3} \left(\frac{\left(\sqrt{C_{1} + 3} + 2\right) \left(\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}\right)}{4} - \frac{1}{2 \left(C_{1} + 3\right)} + \frac{\sqrt{C_{1} + 3} + 2}{2 \left(C_{1} + 3\right)^{\frac{3}{2}}} - \frac{1}{\left(C_{1} + 3\right)^{\frac{3}{2}}}\right)}{6} + \frac{x^{4} \left(\frac{3 \left(\sqrt{C_{1} + 3} + 2\right) \left(\frac{1}{\left(C_{1} + 3\right)^{2}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{4} + \frac{\left(\sqrt{C_{1} + 3} + 2\right) \left(3 \left(\sqrt{C_{1} + 3} + 2\right) \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right) + \frac{6}{\left(C_{1} + 3\right)^{2}} + \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{\sqrt{C_{1} + 3}} - \frac{6 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{12}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{8} - \frac{3}{2 \left(C_{1} + 3\right)^{2}} - \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{4 \sqrt{C_{1} + 3}} + \frac{3 \left(\sqrt{C_{1} + 3} + 2\right)}{2 \left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{3}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{24} + \frac{x^{5} \left(\frac{15 \left(\sqrt{C_{1} + 3} + 2\right) \left(\frac{1}{\left(C_{1} + 3\right)^{3}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{7}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right)}{4} + \frac{\left(\sqrt{C_{1} + 3} + 2\right) \left(15 \left(\sqrt{C_{1} + 3} + 2\right) \left(- \frac{1}{\left(C_{1} + 3\right)^{3}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{7}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right) + \frac{30}{\left(C_{1} + 3\right)^{3}} - \frac{3 \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{\sqrt{C_{1} + 3}} + \frac{3 \left(\frac{1}{\left(C_{1} + 3\right)^{2}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{\sqrt{C_{1} + 3}} + \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{\left(C_{1} + 3\right)^{\frac{3}{2}}} - \frac{30 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{7}{2}}} + \frac{60}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right)}{8} + \frac{\left(\sqrt{C_{1} + 3} + 2\right) \left(30 \left(\sqrt{C_{1} + 3} + 2\right) \left(- \frac{1}{\left(C_{1} + 3\right)^{3}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{7}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right) + \left(\sqrt{C_{1} + 3} + 2\right) \left(15 \left(\sqrt{C_{1} + 3} + 2\right) \left(\frac{1}{\left(C_{1} + 3\right)^{3}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{7}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right) - \frac{30}{\left(C_{1} + 3\right)^{3}} + \frac{6 \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{\sqrt{C_{1} + 3}} - \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{30 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{7}{2}}} - \frac{60}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right) + \frac{60}{\left(C_{1} + 3\right)^{3}} - \frac{6 \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{\sqrt{C_{1} + 3}} + \frac{6 \left(\frac{1}{\left(C_{1} + 3\right)^{2}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{\sqrt{C_{1} + 3}} + \frac{3 \left(\sqrt{C_{1} + 3} + 2\right) \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right) + \frac{6}{\left(C_{1} + 3\right)^{2}} + \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{\sqrt{C_{1} + 3}} - \frac{6 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{12}{\left(C_{1} + 3\right)^{\frac{5}{2}}}}{\sqrt{C_{1} + 3}} + \frac{2 \left(\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}\right)}{\left(C_{1} + 3\right)^{\frac{3}{2}}} - \frac{60 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{7}{2}}} + \frac{120}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right)}{16} - \frac{15}{2 \left(C_{1} + 3\right)^{3}} - \frac{3 \left(\frac{1}{\left(C_{1} + 3\right)^{2}} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right)}{2 \sqrt{C_{1} + 3}} - \frac{3 \left(\sqrt{C_{1} + 3} + 2\right) \left(- \frac{1}{\left(C_{1} + 3\right)^{2}} + \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{5}{2}}} - \frac{2}{\left(C_{1} + 3\right)^{\frac{5}{2}}}\right) + \frac{6}{\left(C_{1} + 3\right)^{2}} + \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{\sqrt{C_{1} + 3}} - \frac{6 \left(\sqrt{C_{1} + 3} + 2\right)}{\left(C_{1} + 3\right)^{\frac{5}{2}}} + \frac{12}{\left(C_{1} + 3\right)^{\frac{5}{2}}}}{8 \sqrt{C_{1} + 3}} - \frac{\frac{1}{C_{1} + 3} - \frac{\sqrt{C_{1} + 3} + 2}{\left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{2}{\left(C_{1} + 3\right)^{\frac{3}{2}}}}{4 \left(C_{1} + 3\right)^{\frac{3}{2}}} + \frac{15 \left(\sqrt{C_{1} + 3} + 2\right)}{2 \left(C_{1} + 3\right)^{\frac{7}{2}}} - \frac{15}{\left(C_{1} + 3\right)^{\frac{7}{2}}}\right)}{120} + 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, 17.258783840525425)
(-5.555555555555555, 36.23670348301979)
(-3.333333333333333, 57.68375892798329)
(-1.1111111111111107, 81.59995017541594)
(1.1111111111111107, 107.98527722531772)
(3.333333333333334, 136.83974007768865)
(5.555555555555557, 168.1633387325287)
(7.777777777777779, 201.9560731898379)
(10.0, 238.2179434496162)
(10.0, 238.2179434496162)