Sr Examen
Ecuación diferencial dx*(-2*x*y^2+6*x)-dy*(2*x^2*y-6*y)=0
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Solución
Ha introducido
[src]
2 d 2 d
6*x - 2*x*y (x) + 6*--(y(x))*y(x) - 2*x *--(y(x))*y(x) = 0
dx dx
$$- 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 x y^{2}{\left(x \right)} + 6 x + 6 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-2*x^2*y*y' - 2*x*y^2 + 6*x + 6*y*y' = 0
Respuesta
[src]
___________
/ 2
/ C1 + 3*x
y(x) = - / ---------
/ 2
\/ -3 + x
$$y{\left(x \right)} = - \sqrt{\frac{C_{1} + 3 x^{2}}{x^{2} - 3}}$$
___________
/ 2
/ C1 + 3*x
y(x) = / ---------
/ 2
\/ -3 + x
$$y{\left(x \right)} = \sqrt{\frac{C_{1} + 3 x^{2}}{x^{2} - 3}}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -2.0218128888515e-09)
(-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, 5.107659831618641e-38)
(7.777777777777779, 8.388243567735217e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)