Sr Examen
Ecuación diferencial y'''-8y''+16y'=64(1-x^2)
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Solución
Ha introducido
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2 3
d d d 2
- 8*---(y(x)) + 16*--(y(x)) + ---(y(x)) = 64 - 64*x
2 dx 3
dx dx
$$16 \frac{d}{d x} y{\left(x \right)} - 8 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 64 - 64 x^{2}$$
16*y' - 8*y'' + y''' = 64 - 64*x^2
Respuesta
[src]
3
2 4*x 5*x 4*x
y(x) = C1 - 2*x - ---- + --- + (C2 + C3*x)*e
3 2
$$y{\left(x \right)} = C_{1} - \frac{4 x^{3}}{3} - 2 x^{2} + \frac{5 x}{2} + \left(C_{2} + C_{3} x\right) e^{4 x}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral