Sr Examen
Ecuación diferencial y''-4y'+7y=(e^x)((3x^3)+2x+1)
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Solución
Ha introducido
[src]
2
d d / 3\ x
- 4*--(y(x)) + 7*y(x) + ---(y(x)) = \1 + 2*x + 3*x /*e
dx 2
dx
$$7 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(3 x^{3} + 2 x + 1\right) e^{x}$$
7*y - 4*y' + y'' = (3*x^3 + 2*x + 1)*exp(x)
Respuesta
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/ 3 2 \
| 1 x 3*x 9*x / / ___\ / ___\\ x| x
y(x) = |- -- + - + ---- + ---- + \C1*sin\x*\/ 3 / + C2*cos\x*\/ 3 //*e |*e
\ 16 2 4 8 /
$$y{\left(x \right)} = \left(\frac{3 x^{3}}{4} + \frac{9 x^{2}}{8} + \frac{x}{2} + \left(C_{1} \sin{\left(\sqrt{3} x \right)} + C_{2} \cos{\left(\sqrt{3} x \right)}\right) e^{x} - \frac{1}{16}\right) e^{x}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral