What is the solution for y^{'''}-3y^'-2y=9e^{-x} ?

The solution for y^{'''}-3y^'-2y=9e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}-(3e^{-x}x^2)/2

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y^{'''}-3y^'-2y=9e^{-x}

y^{^{'''}} - 3 y^{^{'}} - 2 y = 9 e^{- x}

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

Solution steps

y^{'''} (x) - 3 y^{'} (x) - 2 y = 9 e^{- x}

Solve linear ODE:

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

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

What is the solution for y^{'''}-3y^'-2y=9e^{-x} ?
The solution for y^{'''}-3y^'-2y=9e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}-(3e^{-x}x^2)/2