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

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

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y^{''}=y^'+2y+9e^{2x}

y^{^{''}} = y^{^{'}} + 2 y + 9 e^{2 x}

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

Solution steps

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

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

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