Sr Examen
Ecuación diferencial y''-8y'+25y=5x^3e^-x-7e^-x
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
d d -x 3 -x
- 8*--(y(x)) + 25*y(x) + ---(y(x)) = - 7*e + 5*x *e
dx 2
dx
$$25 y{\left(x \right)} - 8 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 5 x^{3} e^{- x} - 7 e^{- x}$$
25*y - 8*y' + y'' = 5*x^3*exp(-x) - 7*exp(-x)
Respuesta
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-x 3 -x 2 -x -x
33191*e 4*x 5*x *e 75*x *e 495*x*e
y(x) = - --------- + (C1*sin(3*x) + C2*cos(3*x))*e + -------- + --------- + ---------
167042 34 578 9826
$$y{\left(x \right)} = \frac{5 x^{3} e^{- x}}{34} + \frac{75 x^{2} e^{- x}}{578} + \frac{495 x e^{- x}}{9826} + \left(C_{1} \sin{\left(3 x \right)} + C_{2} \cos{\left(3 x \right)}\right) e^{4 x} - \frac{33191 e^{- x}}{167042}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral