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

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

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(dy)/(dx)=x^2+x^2y^2

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

y = tan (\frac{x ^{3}}{3} + c_{1})

Solution steps

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

Solve separable ODE:

y = tan (\frac{x ^{3}}{3} + c_{1})

y = tan (\frac{x ^{3}}{3} + c_{1})

\frac{d y}{d x} + 4 y = 3, y (0) = 0

\frac{d y}{d x} = y^{2} - 6

\frac{d y}{d x} = \frac{x ( y - 4 ) + y - 4}{x ( y - 6 ) - 3 ( y - 6 )}

\frac{d y}{d x} = y^{2} + 4 y + 5

\frac{d y}{y ^{2}} = \frac{d x}{- x ^{2} + 4}

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