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

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

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(dy)/(dx)=3x^2(1+y^2)^{3/2}

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

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

Solution steps

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

Solve separable ODE:

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

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