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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d r ( θ )}{r ( θ )} = \frac{r ( θ ) d θ}{θ ^{2}}

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

y^{^{'}} = 0.2 x y

y^{^{'}} = \frac{y cos ( x )}{1 - 2 y}

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

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