Sr Examen
Ecuación diferencial y'''-4y''+5y'-2y=exp(2x)-2*exp(x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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2 3
d d d x 2*x
- 4*---(y(x)) - 2*y(x) + 5*--(y(x)) + ---(y(x)) = - 2*e + e
2 dx 3
dx dx
$$- 2 y{\left(x \right)} + 5 \frac{d}{d x} y{\left(x \right)} - 4 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = e^{2 x} - 2 e^{x}$$
-2*y + 5*y' - 4*y'' + y''' = exp(2*x) - 2*exp(x)
Respuesta
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/ x / x\\ x y(x) = \C1 + C3*e + x*\C2 + x + e //*e
$$y{\left(x \right)} = \left(C_{1} + C_{3} e^{x} + x \left(C_{2} + x + e^{x}\right)\right) e^{x}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral