Sr Examen
Ecuación diferencial y''''+y'''+2y''+2y'=2-xe^-x
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 3 4
d d d d -x
2*--(y(x)) + 2*---(y(x)) + ---(y(x)) + ---(y(x)) = 2 - x*e
dx 2 3 4
dx dx dx
$$2 \frac{d}{d x} y{\left(x \right)} + 2 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} + \frac{d^{4}}{d x^{4}} y{\left(x \right)} = - x e^{- x} + 2$$
2*y' + 2*y'' + y''' + y'''' = -x*exp(-x) + 2
Respuesta
[src]
/ 2 \
/ ___\ / ___\ | x 5*x| -x
y(x) = C1 + x + C3*sin\x*\/ 2 / + C4*cos\x*\/ 2 / + |C2 + -- + ---|*e
\ 6 9 /
$$y{\left(x \right)} = C_{1} + C_{3} \sin{\left(\sqrt{2} x \right)} + C_{4} \cos{\left(\sqrt{2} x \right)} + x + \left(C_{2} + \frac{x^{2}}{6} + \frac{5 x}{9}\right) e^{- x}$$
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