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