Sr Examen
Ecuación diferencial y"-4y'+5y=3*e^(-x)+2x^2
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Solución
Ha introducido
[src]
2
d d 2 -x
- 4*--(y(x)) + 5*y(x) + ---(y(x)) = 2*x + 3*e
dx 2
dx
$$5 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 2 x^{2} + 3 e^{- x}$$
5*y - 4*y' + y'' = 2*x^2 + 3*exp(-x)
Respuesta
[src]
2 -x
44 2*x 3*e 16*x 2*x
y(x) = --- + ---- + ----- + ---- + (C1*sin(x) + C2*cos(x))*e
125 5 10 25
$$y{\left(x \right)} = \frac{2 x^{2}}{5} + \frac{16 x}{25} + \left(C_{1} \sin{\left(x \right)} + C_{2} \cos{\left(x \right)}\right) e^{2 x} + \frac{44}{125} + \frac{3 e^{- x}}{10}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral