Sr Examen
Ecuación diferencial y’’+2y’+5y=e^2x(9x-7)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
d d 2
2*--(y(x)) + 5*y(x) + ---(y(x)) = x*(-7 + 9*x)*e
dx 2
dx
$$5 y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x \left(9 x - 7\right) e^{2}$$
5*y + 2*y' + y'' = x*(9*x - 7)*exp(2)
Respuesta
[src]
2 2 2 2
52*e -x 71*x*e 9*x *e
y(x) = ----- + (C1*sin(2*x) + C2*cos(2*x))*e - ------- + -------
125 25 5
$$y{\left(x \right)} = \frac{9 x^{2} e^{2}}{5} - \frac{71 x e^{2}}{25} + \left(C_{1} \sin{\left(2 x \right)} + C_{2} \cos{\left(2 x \right)}\right) e^{- x} + \frac{52 e^{2}}{125}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral