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Ecuación x^3+3x^2-x-3=0
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Ecuación x^3-6x^2+11x-6=0
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Ecuación x/4+x=12
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Ecuación x+4=-1
- Expresar {x} en función de y en la ecuación:
- 9*x-1*y=17
- 10*x-2*y=11
- -18*x-13*y=2
- -12*x-8*y=13
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Expresiones idénticas
- d^ dos *y/((d*x^ dos))+y=(tres *x+ uno)*cos(x)+((- tres)*x- dos)*sin(x)
- d al cuadrado multiplicar por y dividir por ((d multiplicar por x al cuadrado )) más y es igual a (3 multiplicar por x más 1) multiplicar por coseno de (x) más (( menos 3) multiplicar por x menos 2) multiplicar por seno de (x)
- d en el grado dos multiplicar por y dividir por ((d multiplicar por x en el grado dos)) más y es igual a (tres multiplicar por x más uno) multiplicar por coseno de (x) más (( menos tres) multiplicar por x menos dos) multiplicar por seno de (x)
- d2*y/((d*x2))+y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x)
- d2*y/d*x2+y=3*x+1*cosx+-3*x-2*sinx
- d²*y/((d*x²))+y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x)
- d en el grado 2*y/((d*x en el grado 2))+y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x)
- d^2y/((dx^2))+y=(3x+1)cos(x)+((-3)x-2)sin(x)
- d2y/((dx2))+y=(3x+1)cos(x)+((-3)x-2)sin(x)
- d2y/dx2+y=3x+1cosx+-3x-2sinx
- d^2y/dx^2+y=3x+1cosx+-3x-2sinx
- d^2*y dividir por ((d*x^2))+y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x)
-
Expresiones semejantes
- d^2*y/((d*x^2))+y=(3*x+1)*cos(x)-((-3)*x-2)*sin(x)
- d^2*y/((d*x^2))+y=(3*x+1)*cos(x)+((-3)*x+2)*sin(x)
- d^2*y/((d*x^2))-y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x)
- d^2*y/((d*x^2))+y=(3*x+1)*cos(x)+((3)*x-2)*sin(x)
- d^2*y/((d*x^2))+y=(3*x-1)*cos(x)+((-3)*x-2)*sin(x)
- d^2*y/((d*x^2))+y=(3*x+1)*cosx+((-3)*x-2)*sinx
-
Expresiones con funciones
- Coseno cos
- cos(x)+sin(3x)=0
- cos(x)=2*x
- cos(x)-e^(-x)+x-1=0
- cos(2x)-3*cos(x)+2=0
- cos3b-ctg6bsin3b
- Seno sin
- sin(x)=1.5
- sin(sin(x))=1
- sin(x)=-0.5
- sin(-x)=1/2
- sin(x)=4/3
d^2*y/((d*x^2))+y=(3*x+1)*cos(x)+((-3)*x-2)*sin(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 d *y ---- + y = (3*x + 1)*cos(x) + (-3*x - 2)*sin(x) 2 d*x
$$y + \frac{d^{2} y}{d x^{2}} = \left(- 3 x - 2\right) \sin{\left(x \right)} + \left(3 x + 1\right) \cos{\left(x \right)}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\frac{d y}{x^{2}} + y = \left(- 3 x - 2\right) \sin{\left(x \right)} + \left(3 x + 1\right) \cos{\left(x \right)}$$
Коэффициент при y равен
$$\frac{d}{x^{2}} + 1$$
entonces son posibles los casos para d :
$$d < - x^{2}$$
$$d = - x^{2}$$
Consideremos todos los casos con detalles:
Con
$$d < - x^{2}$$
la ecuación será
$$y - \left(- 3 x - 2\right) \sin{\left(x \right)} - \left(3 x + 1\right) \cos{\left(x \right)} + \frac{y \left(- x^{2} - 1\right)}{x^{2}} = 0$$
su solución
$$y = x^{2} \left(- 3 \sqrt{2} x \cos{\left(x + \frac{\pi}{4} \right)} + 2 \sin{\left(x \right)} - \cos{\left(x \right)}\right)$$
Con
$$d = - x^{2}$$
la ecuación será
$$- \left(- 3 x - 2\right) \sin{\left(x \right)} - \left(3 x + 1\right) \cos{\left(x \right)} = 0$$
su solución
$$\frac{d y}{x^{2}} + y = \left(- 3 x - 2\right) \sin{\left(x \right)} + \left(3 x + 1\right) \cos{\left(x \right)}$$
Коэффициент при y равен
$$\frac{d}{x^{2}} + 1$$
entonces son posibles los casos para d :
$$d < - x^{2}$$
$$d = - x^{2}$$
Consideremos todos los casos con detalles:
Con
$$d < - x^{2}$$
la ecuación será
$$y - \left(- 3 x - 2\right) \sin{\left(x \right)} - \left(3 x + 1\right) \cos{\left(x \right)} + \frac{y \left(- x^{2} - 1\right)}{x^{2}} = 0$$
su solución
$$y = x^{2} \left(- 3 \sqrt{2} x \cos{\left(x + \frac{\pi}{4} \right)} + 2 \sin{\left(x \right)} - \cos{\left(x \right)}\right)$$
Con
$$d = - x^{2}$$
la ecuación será
$$- \left(- 3 x - 2\right) \sin{\left(x \right)} - \left(3 x + 1\right) \cos{\left(x \right)} = 0$$
su solución
Gráfica
Respuesta rápida
[src]
/ / 2 \ / 2 \\ / 2 \ / 2 \
|/ ___ / / pi\\\ | x | / ___ / / pi\\\ | x || / ___ / / pi\\\ | x | / ___ / / pi\\\ | x |
y1 = I*||cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*im|------| + |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*re|------|| + |cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*re|------| - |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*im|------|
|\ \ \ 4 /// | 2| \ \ \ 4 /// | 2|| \ \ \ 4 /// | 2| \ \ \ 4 /// | 2|
\ \d + x / \d + x // \d + x / \d + x /
$$y_{1} = i \left(\left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)}\right) - \left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)}$$
y1 = i*((-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*sqrt(2)*im(x*cos(x + pi/4)))*re(x^2/(d + x^2)) + (-2*sin(re(x))*cosh(im(x)) + cos(re(x))*cosh(im(x)) + 3*sqrt(2)*re(x*cos(x + pi/4)))*im(x^2/(d + x^2))) - (-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*sqrt(2)*im(x*cos(x + pi/4)))*im(x^2/(d + x^2)) + (-2*sin(re(x))*cosh(im(x)) + cos(re(x))*cosh(im(x)) + 3*sqrt(2)*re(x*cos(x + pi/4)))*re(x^2/(d + x^2))
Suma y producto de raíces
[src]
suma
/ / 2 \ / 2 \\ / 2 \ / 2 \ |/ ___ / / pi\\\ | x | / ___ / / pi\\\ | x || / ___ / / pi\\\ | x | / ___ / / pi\\\ | x | I*||cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*im|------| + |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*re|------|| + |cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*re|------| - |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*im|------| |\ \ \ 4 /// | 2| \ \ \ 4 /// | 2|| \ \ \ 4 /// | 2| \ \ \ 4 /// | 2| \ \d + x / \d + x // \d + x / \d + x /
$$i \left(\left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)}\right) - \left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)}$$
=
/ / 2 \ / 2 \\ / 2 \ / 2 \ |/ ___ / / pi\\\ | x | / ___ / / pi\\\ | x || / ___ / / pi\\\ | x | / ___ / / pi\\\ | x | I*||cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*im|------| + |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*re|------|| + |cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*re|------| - |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*im|------| |\ \ \ 4 /// | 2| \ \ \ 4 /// | 2|| \ \ \ 4 /// | 2| \ \ \ 4 /// | 2| \ \d + x / \d + x // \d + x / \d + x /
$$i \left(\left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)}\right) - \left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)}$$
producto
/ / 2 \ / 2 \\ / 2 \ / 2 \ |/ ___ / / pi\\\ | x | / ___ / / pi\\\ | x || / ___ / / pi\\\ | x | / ___ / / pi\\\ | x | I*||cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*im|------| + |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*re|------|| + |cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*re|------| - |-sin(re(x))*sinh(im(x)) - 2*cos(re(x))*sinh(im(x)) + 3*\/ 2 *im|x*cos|x + --|||*im|------| |\ \ \ 4 /// | 2| \ \ \ 4 /// | 2|| \ \ \ 4 /// | 2| \ \ \ 4 /// | 2| \ \d + x / \d + x // \d + x / \d + x /
$$i \left(\left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)}\right) - \left(- \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)}$$
=
/ / 2 \ / 2 \\ / 2 \ / 2 \ |/ ___ / / pi\\\ | x | / ___ / / pi\\ \ | x || / ___ / / pi\\\ | x | / ___ / / pi\\ \ | x | I*||cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*im|------| - |sin(re(x))*sinh(im(x)) - 3*\/ 2 *im|x*cos|x + --|| + 2*cos(re(x))*sinh(im(x))|*re|------|| + |cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*\/ 2 *re|x*cos|x + --|||*re|------| + |sin(re(x))*sinh(im(x)) - 3*\/ 2 *im|x*cos|x + --|| + 2*cos(re(x))*sinh(im(x))|*im|------| |\ \ \ 4 /// | 2| \ \ \ 4 // / | 2|| \ \ \ 4 /// | 2| \ \ \ 4 // / | 2| \ \d + x / \d + x // \d + x / \d + x /
$$i \left(- \left(\sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)}\right) + \left(\sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - 3 \sqrt{2} \operatorname{im}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{im}{\left(\frac{x^{2}}{d + x^{2}}\right)} + \left(- 2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} + 3 \sqrt{2} \operatorname{re}{\left(x \cos{\left(x + \frac{\pi}{4} \right)}\right)}\right) \operatorname{re}{\left(\frac{x^{2}}{d + x^{2}}\right)}$$
i*((cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*sqrt(2)*re(x*cos(x + pi/4)))*im(x^2/(d + x^2)) - (sin(re(x))*sinh(im(x)) - 3*sqrt(2)*im(x*cos(x + pi/4)) + 2*cos(re(x))*sinh(im(x)))*re(x^2/(d + x^2))) + (cos(re(x))*cosh(im(x)) - 2*cosh(im(x))*sin(re(x)) + 3*sqrt(2)*re(x*cos(x + pi/4)))*re(x^2/(d + x^2)) + (sin(re(x))*sinh(im(x)) - 3*sqrt(2)*im(x*cos(x + pi/4)) + 2*cos(re(x))*sinh(im(x)))*im(x^2/(d + x^2))