What is the solution for (dy)/(dx)=(3x^2-6x^2y^2)/(y-x^3y) ?

The solution for (dy)/(dx)=(3x^2-6x^2y^2)/(y-x^3y) is

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(dy)/(dx)=(3x^2-6x^2y^2)/(y-x^3y)

\frac{d y}{d x} = \frac{3 x ^{2} - 6 x ^{2} y ^{2}}{y - x ^{3} y}

y = \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}, y = - \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}

Solution steps

\frac{d y}{d x} = \frac{3 x ^{2} - 6 x ^{2} y ^{2}}{y - x ^{3} y}

Solve separable ODE:

y = \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}, y = - \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}

y = \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}, y = - \frac{e ^{4 c_{1}} x ^{12} + e ^{4 c_{1}} + 1 - 4 e ^{4 c_{1}} x ^{9} + 6 e ^{4 c_{1}} x ^{6} - 4 e ^{4 c_{1}} x ^{3}}{2}

What is the solution for (dy)/(dx)=(3x^2-6x^2y^2)/(y-x^3y) ?
The solution for (dy)/(dx)=(3x^2-6x^2y^2)/(y-x^3y) is