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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = cos (x) sec (y)

y^{^{'}} (x) = \frac{y cos ( x )}{1 + 3 y ^{3}}, y (0) = 1

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

(8 + x) \frac{d y}{d x} = 5 y

\frac{d y}{d x} + 7 x y = 8 x, y (0) = 6

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