Sr Examen
Ecuación diferencial (xy^2+x)dx-(y-x^2y)dy=0
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Solución
Ha introducido
[src]
2 d 2 d
x + x*y (x) - --(y(x))*y(x) + x *--(y(x))*y(x) = 0
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} + x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' + x*y^2 + x - y*y' = 0
Respuesta
[src]
_________
/ 2
/ C1 - x
y(x) = - / -------
/ 2
\/ -1 + x
$$y{\left(x \right)} = - \sqrt{\frac{C_{1} - x^{2}}{x^{2} - 1}}$$
_________
/ 2
/ C1 - x
y(x) = / -------
/ 2
\/ -1 + x
$$y{\left(x \right)} = \sqrt{\frac{C_{1} - x^{2}}{x^{2} - 1}}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.264934672971488)
(-5.555555555555555, 2.0444311135240114)
(-3.333333333333333, 3.7813720103081265)
(-1.1111111111111107, 25.660451107281414)
(1.1111111111111107, 679614.4948519839)
(3.333333333333334, 6.93056692442215e-310)
(5.555555555555557, 6.9303486443131e-310)
(7.777777777777779, 6.93056692442847e-310)
(10.0, 6.93056692442847e-310)
(10.0, 6.93056692442847e-310)