Sr Examen
Ecuación diferencial y''-8y'+25y=5x^2-e^-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 2
- 8*--(y(x)) + 25*y(x) + ---(y(x)) = - 8*e + 5*x
dx 2
dx
$$25 y{\left(x \right)} - 8 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 5 x^{2} - 8 e^{- x}$$
25*y - 8*y' + y'' = 5*x^2 - 8*exp(-x)
Respuesta
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-x 2
78 4*e x 16*x 4*x
y(x) = ---- - ----- + -- + ---- + (C1*sin(3*x) + C2*cos(3*x))*e
3125 17 5 125
$$y{\left(x \right)} = \frac{x^{2}}{5} + \frac{16 x}{125} + \left(C_{1} \sin{\left(3 x \right)} + C_{2} \cos{\left(3 x \right)}\right) e^{4 x} + \frac{78}{3125} - \frac{4 e^{- x}}{17}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral