What is the solution for y^{''}+y^'=e^{-x}+3x^2 ?

The solution for y^{''}+y^'=e^{-x}+3x^2 is y=c_{1}+c_{2}e^{-x}-e^{-x}x+x^3-3x^2+6x

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y^{''}+y^'=e^{-x}+3x^2

y^{^{''}} + y^{^{'}} = e^{- x} + 3 x^{2}

y = c_{1} + c_{2} e^{- x} - e^{- x} x + x^{3} - 3 x^{2} + 6 x

Solution steps

y^{''} (x) + y^{'} (x) = e^{- x} + 3 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} - e^{- x} x + x^{3} - 3 x^{2} + 6 x

y = c_{1} + c_{2} e^{- x} - e^{- x} x + x^{3} - 3 x^{2} + 6 x

What is the solution for y^{''}+y^'=e^{-x}+3x^2 ?
The solution for y^{''}+y^'=e^{-x}+3x^2 is y=c_{1}+c_{2}e^{-x}-e^{-x}x+x^3-3x^2+6x