Sr Examen
Ecuación diferencial (4y+yx^2)dy-(2x-xy^2)dx=0
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Solución
Ha introducido
[src]
2 d 2 d
-2*x + x*y (x) + 4*--(y(x))*y(x) + x *--(y(x))*y(x) = 0
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} - 2 x + 4 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' + x*y^2 - 2*x + 4*y*y' = 0
Respuesta
[src]
___________
/ 2
/ C1 + 2*x
y(x) = - / ---------
/ 2
\/ 4 + x
$$y{\left(x \right)} = - \sqrt{\frac{C_{1} + 2 x^{2}}{x^{2} + 4}}$$
___________
/ 2
/ C1 + 2*x
y(x) = / ---------
/ 2
\/ 4 + x
$$y{\left(x \right)} = \sqrt{\frac{C_{1} + 2 x^{2}}{x^{2} + 4}}$$
Gráfico para el problema de Cauchy
Clasificación
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, 5.050917224471776e-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, 1.3953866364196653e-75)
(7.777777777777779, 8.388243567737083e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)