What is the solution for 3(1+q^2)(dp)/(dq)=2pq(p^3-1) ?

The solution for 3(1+q^2)(dp)/(dq)=2pq(p^3-1) is p=\sqrt[3]{1/(1-q^2e^{3c_{1)}-e^{3c_{1}}}}

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3(1+q^2)(dp)/(dq)=2pq(p^3-1)

3 (1 + q^{2}) \frac{d p}{d q} = 2 pq (p^{3} - 1)

Solution steps

3 (1 + q^{2}) \frac{d p}{d q} = 2 pq (p^{3} - 1)

Solve separable ODE:

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

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

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

\frac{d y}{d x} = 2 x y^{2} + 3 x^{2} y^{2}, y (0) = 5

(x - 1) y^{^{'}} = (4 - y^{2})

What is the solution for 3(1+q^2)(dp)/(dq)=2pq(p^3-1) ?
The solution for 3(1+q^2)(dp)/(dq)=2pq(p^3-1) is p=\sqrt[3]{1/(1-q^2e^{3c_{1)}-e^{3c_{1}}}}