Sr Examen
Ecuación diferencial y'''+3y''+3y'+y=x^(1/2)e^(-x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 3
d d d ___ -x
3*--(y(x)) + 3*---(y(x)) + ---(y(x)) + y(x) = \/ x *e
dx 2 3
dx dx
$$y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + 3 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = \sqrt{x} e^{- x}$$
y + 3*y' + 3*y'' + y''' = sqrt(x)*exp(-x)
Respuesta
[src]
/ / / 3/2\\\
| | | 8*x ||| -x
y(x) = |C1 + x*|C2 + x*|C3 + ------|||*e
\ \ \ 105 ///
$$y{\left(x \right)} = \left(C_{1} + x \left(C_{2} + x \left(C_{3} + \frac{8 x^{\frac{3}{2}}}{105}\right)\right)\right) e^{- x}$$
Clasificación
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral