What is the solution for y^'-x^2cos(y)=x^2 ?

The solution for y^'-x^2cos(y)=x^2 is y=2arctan((x^3)/3+c_{1})+2pin

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y^'-x^2cos(y)=x^2

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

y = 2 arctan (\frac{x ^{3}}{3} + c_{1}) + 2 πn

Solution steps

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

Solve separable ODE:

y = 2 arctan (\frac{x ^{3}}{3} + c_{1}) + 2 πn

y = 2 arctan (\frac{x ^{3}}{3} + c_{1}) + 2 πn

y^{^{'}} = y^{2} x^{2}

\frac{d y}{d x} = 8 x sec (y)

\frac{d y}{d x} = 0.4 x y

\frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

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

What is the solution for y^'-x^2cos(y)=x^2 ?
The solution for y^'-x^2cos(y)=x^2 is y=2arctan((x^3)/3+c_{1})+2pin