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

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

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

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

y = 3 \frac{x ^{2} + 2 x + 1}{x ^{2} + 2 x + 1 - e ^{2 + 2 x + c_{1}}}

Solution steps

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

Solve separable ODE:

y = 3 \frac{x ^{2} + 2 x + 1}{x ^{2} + 2 x + 1 - e ^{2 + 2 x + c_{1}}}

y = 3 \frac{x ^{2} + 2 x + 1}{x ^{2} + 2 x + 1 - e ^{2 + 2 x + c_{1}}}

\frac{d x}{3 sin ( y )} = \frac{4 d y}{5 sin ( x )}

x e^{- y} d y + \frac{x ^{2} + 1}{y} d x = 0

y^{^{'}} y^{1} = - 2 e^{x} y^{2}

\frac{d y}{d x} = y \cdot sin^{3} (x)

y^{^{'}} = \frac{4}{5 x y}

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