Sr Examen
Ecuación diferencial y'(y^2+x+y)+2xy^2-y=0
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Solución
Ha introducido
[src]
/ 2 \ d 2
-y(x) + \x + y (x) + y(x)/*--(y(x)) + 2*x*y (x) = 0
dx
$$2 x y^{2}{\left(x \right)} + \left(x + y^{2}{\left(x \right)} + y{\left(x \right)}\right) \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} = 0$$
2*x*y^2 + (x + y^2 + y)*y' - y = 0
Respuesta
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2 x
x - ---- + log(y(x)) + y(x) = C1
y(x)
$$x^{2} - \frac{x}{y{\left(x \right)}} + y{\left(x \right)} + \log{\left(y{\left(x \right)} \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.14110897002279726)
(-5.555555555555555, 0.06490022584254054)
(-3.333333333333333, 0.03141284296446603)
(-1.1111111111111107, 0.009479639897258866)
(1.1111111111111107, -0.009699480254990265)
(3.333333333333334, -0.032206274080092946)
(5.555555555555557, -0.0668940737474151)
(7.777777777777779, -0.14755828997345338)
(10.0, -0.8223347933707031)
(10.0, -0.8223347933707031)