Sr Examen
Ecuación diferencial x*y+y'=-e^(-x^2)*y^3
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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
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2 / 4\ 3 3 / 4\ 4 / 4 4 / 4\\ 3 5 / 4 4 / 4\ 4 / 4\\
3 C1*x *\-1 + 3*C1 / C1 *x *\7 - 15*C1 / C1*x *\1 - 15*C1 - 7*C1 *\1 - 5*C1 // C1 *x *\-103 + 645*C1 + 42*C1 *\1 - 15*C1 / + 63*C1 *\1 - 5*C1 // / 6\
y(x) = C1 - x*C1 + ------------------ + ------------------- + -------------------------------------- + ------------------------------------------------------------------ + O\x /
2 6 8 120
$$y{\left(x \right)} = C_{1} + \frac{C_{1} x^{2} \left(3 C_{1}^{4} - 1\right)}{2} + \frac{C_{1} x^{4} \left(- 7 C_{1}^{4} \left(1 - 5 C_{1}^{4}\right) - 15 C_{1}^{4} + 1\right)}{8} - C_{1}^{3} x + \frac{C_{1}^{3} x^{3} \left(7 - 15 C_{1}^{4}\right)}{6} + \frac{C_{1}^{3} x^{5} \left(42 C_{1}^{4} \left(1 - 15 C_{1}^{4}\right) + 63 C_{1}^{4} \left(1 - 5 C_{1}^{4}\right) + 645 C_{1}^{4} - 103\right)}{120} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 284261368.7124323)
(-5.555555555555555, 16853057.60125997)
(-3.333333333333333, 675.0545897329089)
(-1.1111111111111107, 2.9728370851809336)
(1.1111111111111107, 0.3429595696041392)
(3.333333333333334, 0.0024417895662934746)
(5.555555555555557, 1.2591410167870492e-07)
(7.777777777777779, -2.434440917821363e-10)
(10.0, -9.20458195489326e-11)
(10.0, -9.20458195489326e-11)