What is the solution for xy^{''}+xy^'=x^3 ?

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

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xy^{''}+xy^'=x^3

x y^{^{''}} + x y^{^{'}} = x^{3}

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} - x^{2} + 2 x

Solution steps

x y^{''} (x) + x y^{'} (x) = x^{3}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} - x^{2} + 2 x

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} - x^{2} + 2 x

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