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