Sr Examen
Ecuación diferencial dx*(6*x^2*y+3*x^2)+dy*(6*x^2*y+4*y^3)=0
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Solución
Ha introducido
[src]
2 3 d 2 2 d
3*x + 4*y (x)*--(y(x)) + 6*x *y(x) + 6*x *--(y(x))*y(x) = 0
dx dx
$$6 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 6 x^{2} y{\left(x \right)} + 3 x^{2} + 4 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
6*x^2*y*y' + 6*x^2*y + 3*x^2 + 4*y^3*y' = 0
Respuesta
[src]
5 3
9*x *(-1 - 2*C1) x *(-1 - 2*C1) / 6\
y(x) = C1 - ---------------- + -------------- + O\x /
5 3
40*C1 4*C1
$$y{\left(x \right)} = - \frac{9 x^{5} \left(- 2 C_{1} - 1\right)}{40 C_{1}^{5}} + \frac{x^{3} \left(- 2 C_{1} - 1\right)}{4 C_{1}^{3}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 4.576241849812193e-11)
(-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, 9.59052908001256e-43)
(7.777777777777779, 8.3882435718278e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)