Sr Examen
Ecuación diferencial 6y^(2)dx-x(2x^3+y)dy=0
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Solución
Ha introducido
[src]
2 4 d d
6*y (x) - 2*x *--(y(x)) - x*--(y(x))*y(x) = 0
dx dx
$$- 2 x^{4} \frac{d}{d x} y{\left(x \right)} - x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 6 y^{2}{\left(x \right)} = 0$$
-2*x^4*y' - x*y*y' + 6*y^2 = 0
Respuesta
[src]
___________________
3 / 2 3\ / 9 / 2 3\
x *\4 + 9*C1 *x / 3*C1*\/ x *\8 + 9*C1 *x /
y(x) = ----------------- - ---------------------------
2 2
$$y{\left(x \right)} = - \frac{3 C_{1} \sqrt{x^{9} \left(9 C_{1}^{2} x^{3} + 8\right)}}{2} + \frac{x^{3} \left(9 C_{1}^{2} x^{3} + 4\right)}{2}$$
___________________
3 / 2 3\ / 9 / 2 3\
x *\4 + 9*C1 *x / 3*C1*\/ x *\8 + 9*C1 *x /
y(x) = ----------------- + ---------------------------
2 2
$$y{\left(x \right)} = \frac{3 C_{1} \sqrt{x^{9} \left(9 C_{1}^{2} x^{3} + 8\right)}}{2} + \frac{x^{3} \left(9 C_{1}^{2} x^{3} + 4\right)}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.750633987065836)
(-5.555555555555555, 0.752731610370807)
(-3.333333333333333, 0.7649978388534808)
(-1.1111111111111107, 2.997758116165166)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.349452126851315e+161)
(7.777777777777779, 8.388243567717305e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)