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

The solution for (y^')/x =2x^2-y is y=4(1/2 x^2-1)+(c_{1}}{e^{\frac{x^2)/2}}

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

\frac{y ^{^{'}}}{x} = 2 x^{2} - y

y = 4 (\frac{1}{2} x^{2} - 1) + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}}}

Solution steps

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

Solve linear ODE:

y = 4 (\frac{1}{2} x^{2} - 1) + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}}}

y = 4 (\frac{1}{2} x^{2} - 1) + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}}}

f (x) = - \frac{4 x}{( x - 2 ) ^{3}}

g (t) = 5 - x

\frac{d}{d x} (e^{- 2 x^{3}})

\int 6 x 3 x + 1 d x

What is the solution for (y^')/x =2x^2-y ?
The solution for (y^')/x =2x^2-y is y=4(1/2 x^2-1)+(c_{1}}{e^{\frac{x^2)/2}}