Sr Examen
Ecuación diferencial y'''-4y''+3y'=x^2+xe^(2x)
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Solución
Ha introducido
[src]
2 3
d d d 2 2*x
- 4*---(y(x)) + 3*--(y(x)) + ---(y(x)) = x + x*e
2 dx 3
dx dx
$$3 \frac{d}{d x} y{\left(x \right)} - 4 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = x^{2} + x e^{2 x}$$
3*y' - 4*y'' + y''' = x^2 + x*exp(2*x)
Respuesta
[src]
3 2 2*x
x 4*x 26*x x 3*x (1 - 2*x)*e
y(x) = C1 + -- + ---- + ---- + C2*e + C3*e + --------------
9 9 27 4
$$y{\left(x \right)} = C_{1} + C_{2} e^{x} + C_{3} e^{3 x} + \frac{x^{3}}{9} + \frac{4 x^{2}}{9} + \frac{26 x}{27} + \frac{\left(1 - 2 x\right) e^{2 x}}{4}$$
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