What is the solution for 3(x^2+1)(dy)/(dx)=2xy(y^3-1) ?

The solution for 3(x^2+1)(dy)/(dx)=2xy(y^3-1) is y=\sqrt[3]{1/(1-x^2e^{3c_{1)}-e^{3c_{1}}}}

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3(x^2+1)(dy)/(dx)=2xy(y^3-1)

3 (x^{2} + 1) \frac{d y}{d x} = 2 x y (y^{3} - 1)

Solution steps

3 (x^{2} + 1) \frac{d y}{d x} = 2 x y (y^{3} - 1)

Solve separable ODE:

\frac{d y}{d x} x y + x = 2

x^{^{'}} = x

y^{^{'}} - 3 x^{2} y = x^{2}

y^{^{'}} = - \frac{x}{4 y}

y^{2} d x + 2 x^{2} d y = 0

What is the solution for 3(x^2+1)(dy)/(dx)=2xy(y^3-1) ?
The solution for 3(x^2+1)(dy)/(dx)=2xy(y^3-1) is y=\sqrt[3]{1/(1-x^2e^{3c_{1)}-e^{3c_{1}}}}