Sr Examen
Ecuación diferencial y''+2y'+5y=x^2-5x+2+e^(x)
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Solución
Ha introducido
[src]
2
d d 2 x
2*--(y(x)) + 5*y(x) + ---(y(x)) = 2 + x - 5*x + e
dx 2
dx
$$5 y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x^{2} - 5 x + e^{x} + 2$$
5*y + 2*y' + y'' = x^2 - 5*x + exp(x) + 2
Respuesta
[src]
2 x
98 29*x x e -x
y(x) = --- - ---- + -- + -- + (C1*sin(2*x) + C2*cos(2*x))*e
125 25 5 8
$$y{\left(x \right)} = \frac{x^{2}}{5} - \frac{29 x}{25} + \left(C_{1} \sin{\left(2 x \right)} + C_{2} \cos{\left(2 x \right)}\right) e^{- x} + \frac{e^{x}}{8} + \frac{98}{125}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral