Sr Examen
Ecuación diferencial d^2*y/((d*x^2))-4(dy/dx)+20y=(2x+8)*e^(5x)
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Solución
Ha introducido
[src]
2
d d 5*x
- 4*--(y(x)) + 20*y(x) + ---(y(x)) = (8 + 2*x)*e
dx 2
dx
$$20 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(2 x + 8\right) e^{5 x}$$
20*y - 4*y' + y'' = (2*x + 8)*exp(5*x)
Respuesta
[src]
/ 3*x 3*x\
|188*e 2*x*e | 2*x
y(x) = |-------- + C1*sin(4*x) + C2*cos(4*x) + --------|*e
\ 625 25 /
$$y{\left(x \right)} = \left(C_{1} \sin{\left(4 x \right)} + C_{2} \cos{\left(4 x \right)} + \frac{2 x e^{3 x}}{25} + \frac{188 e^{3 x}}{625}\right) e^{2 x}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral