What is the solution for y^{''}+2y^'-3y=8e^{-3x} ?

The solution for y^{''}+2y^'-3y=8e^{-3x} is y=c_{1}e^x+c_{2}e^{-3x}-2xe^{-3x}

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y^{''}+2y^'-3y=8e^{-3x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 e^{- 3 x}

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

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 8 e^{- 3 x}

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'-3y=8e^{-3x} ?
The solution for y^{''}+2y^'-3y=8e^{-3x} is y=c_{1}e^x+c_{2}e^{-3x}-2xe^{-3x}