Sr Examen
Ecuación diferencial 6xdx-2ydy=2y(x)^2dy-3x(y)^2dx
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Solución
Ha introducido
[src]
d 2 2 d
6*x - 2*--(y(x))*y(x) = - 3*x*y (x) + 2*x *--(y(x))*y(x)
dx dx
$$6 x - 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)}$$
6*x - 2*y*y' = 2*x^2*y*y' - 3*x*y^2
Respuesta
[src]
_______________________________________________
/ ________ ________
/ / 2 2*C1 2 / 2 2*C1
y(x) = -\/ -2 + \/ 1 + x *e + x *\/ 1 + x *e
$$y{\left(x \right)} = - \sqrt{x^{2} \sqrt{x^{2} + 1} e^{2 C_{1}} + \sqrt{x^{2} + 1} e^{2 C_{1}} - 2}$$
_______________________________________________
/ ________ ________
/ / 2 2*C1 2 / 2 2*C1
y(x) = \/ -2 + \/ 1 + x *e + x *\/ 1 + x *e
$$y{\left(x \right)} = \sqrt{x^{2} \sqrt{x^{2} + 1} e^{2 C_{1}} + \sqrt{x^{2} + 1} e^{2 C_{1}} - 2}$$
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, -2.467323757547773e-08)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 2.5910489201161894e+184)
(7.777777777777779, 8.388243567737008e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)