Sr Examen
Ecuación diferencial (3*(x^2)+6*x*y)dx+(6*(x^2)*y+4*(y^3))dy=0
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Solución
Ha introducido
[src]
2 3 d 2 d
3*x + 4*y (x)*--(y(x)) + 6*x*y(x) + 6*x *--(y(x))*y(x) = 0
dx dx
$$6 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} + 6 x y{\left(x \right)} + 4 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
6*x^2*y*y' + 3*x^2 + 6*x*y + 4*y^3*y' = 0
Respuesta
[src]
5 / 117 \ 4 / 1 \
2 3 x *|27 - ----| 9*x *|1 - --|
3*x x \ 2*C1/ \ C1/ / 6\
y(x) = C1 - ----- - ----- + -------------- + ------------- + O\x /
2 3 5 4
4*C1 4*C1 120*C1 16*C1
$$y{\left(x \right)} = \frac{x^{5} \left(27 - \frac{117}{2 C_{1}}\right)}{120 C_{1}^{5}} + \frac{9 x^{4} \left(1 - \frac{1}{C_{1}}\right)}{16 C_{1}^{4}} - \frac{x^{3}}{4 C_{1}^{3}} - \frac{3 x^{2}}{4 C_{1}^{2}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -9.992979365565327e-10)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 2.6509947707452356e-52)
(7.777777777777779, 8.388243571827865e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)