Sr Examen
Ecuación diferencial dx*(-9*(x^2)*(y^2)+2*x)+(-6*(x^3)*y+4*(y^3))*dy=0
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Solución
Ha introducido
[src]
2 2 3 d 3 d
2*x - 9*x *y (x) + 4*y (x)*--(y(x)) - 6*x *--(y(x))*y(x) = 0
dx dx
$$- 6 x^{3} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 9 x^{2} y^{2}{\left(x \right)} + 2 x + 4 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-6*x^3*y*y' - 9*x^2*y^2 + 2*x + 4*y^3*y' = 0
Respuesta
[src]
4 2 3 5
3*x x 3*x 3*x / 6\
y(x) = C1 - ------ - ----- + ---- + ------ + O\x /
7 3 4*C1 5
32*C1 4*C1 16*C1
$$y{\left(x \right)} = - \frac{3 x^{4}}{32 C_{1}^{7}} + \frac{3 x^{5}}{16 C_{1}^{5}} - \frac{x^{2}}{4 C_{1}^{3}} + \frac{3 x^{3}}{4 C_{1}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.1057445931792054)
(-5.555555555555555, 1.8420460250333712)
(-3.333333333333333, 3.765707966784033)
(-1.1111111111111107, 6.345109879889329)
(1.1111111111111107, 6.661504555867182)
(3.333333333333334, 11.193375838792345)
(5.555555555555557, 22.755140510406825)
(7.777777777777779, 37.58650431132551)
(10.0, 54.77739029443711)
(10.0, 54.77739029443711)