Sr Examen
Ecuación diferencial -x*y+y'=-e^(-x^2)*y^3
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
d 3 -x
-x*y(x) + --(y(x)) = -y (x)*e
dx
$$- x y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = - y^{3}{\left(x \right)} e^{- x^{2}}$$
-x*y + y' = -y^3*exp(-x^2)
Respuesta
[src]
2 / 4\ 3 3 / 4\ 4 / 4 4 / 4\\ 3 5 / 4 4 / 4\ 4 / 4\\
3 C1*x *\1 + 3*C1 / C1 *x *\-1 - 5*C1 / C1*x *\1 + 3*C1 - C1 *\-3 - 35*C1 // C1 *x *\-5 - 35*C1 + 3*C1 *\-3 - 35*C1 / + 6*C1 *\-1 - 35*C1 // / 6\
y(x) = C1 - x*C1 + ----------------- + ------------------- + ------------------------------------- + ---------------------------------------------------------------- + O\x /
2 2 8 40
$$y{\left(x \right)} = C_{1} + \frac{C_{1} x^{2} \left(3 C_{1}^{4} + 1\right)}{2} + \frac{C_{1} x^{4} \left(- C_{1}^{4} \left(- 35 C_{1}^{4} - 3\right) + 3 C_{1}^{4} + 1\right)}{8} - C_{1}^{3} x + \frac{C_{1}^{3} x^{3} \left(- 5 C_{1}^{4} - 1\right)}{2} + \frac{C_{1}^{3} x^{5} \left(3 C_{1}^{4} \left(- 35 C_{1}^{4} - 3\right) + 6 C_{1}^{4} \left(- 35 C_{1}^{4} - 1\right) - 35 C_{1}^{4} - 5\right)}{40} + O\left(x^{6}\right)$$
Clasificación
1st power series
lie group