Sr Examen
Ecuación diferencial y'=y-xy^3
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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d 3 --(y(x)) = - x*y (x) + y(x) dx
$$\frac{d}{d x} y{\left(x \right)} = - x y^{3}{\left(x \right)} + y{\left(x \right)}$$
y' = -x*y^3 + y
Respuesta
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2 / 2\ 3 / 2\ 4 / 2 4 2 / 2\\ 5 / 2 4 2 / 2\ 2 / 2\ 2 / 2\\
C1*x *\1 - C1 / C1*x *\1 - 7*C1 / C1*x *\1 - 33*C1 + 6*C1 - C1 *\1 - 3*C1 // C1*x *\1 - 99*C1 + 90*C1 - C1 *\1 - 21*C1 / - 3*C1 *\1 - 3*C1 / + 3*C1 *\-13 + 15*C1 // / 6\
y(x) = C1 + C1*x + --------------- + ----------------- + -------------------------------------------- + ----------------------------------------------------------------------------------------- + O\x /
2 6 24 120
$$y{\left(x \right)} = C_{1} + C_{1} x + \frac{C_{1} x^{2} \left(1 - C_{1}^{2}\right)}{2} + \frac{C_{1} x^{3} \left(1 - 7 C_{1}^{2}\right)}{6} + \frac{C_{1} x^{4} \left(6 C_{1}^{4} - C_{1}^{2} \left(1 - 3 C_{1}^{2}\right) - 33 C_{1}^{2} + 1\right)}{24} + \frac{C_{1} x^{5} \left(90 C_{1}^{4} - C_{1}^{2} \left(1 - 21 C_{1}^{2}\right) - 3 C_{1}^{2} \left(1 - 3 C_{1}^{2}\right) + 3 C_{1}^{2} \left(15 C_{1}^{2} - 13\right) - 99 C_{1}^{2} + 1\right)}{120} + O\left(x^{6}\right)$$
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, 18995.062402090127)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 8.609893872819149e-43)
(7.777777777777779, 8.38824356733775e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)