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

The solution for y^{''}+2y^'+y=-e^{2x}+e^{3x} is y=c_{1}e^{-x}+c_{2}xe^{-x}-1/9 e^{2x}+1/16 e^{3x}

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

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

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{9} e^{2 x} + \frac{1}{16} e^{3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{9} e^{2 x} + \frac{1}{16} e^{3 x}

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{9} e^{2 x} + \frac{1}{16} e^{3 x}

What is the solution for y^{''}+2y^'+y=-e^{2x}+e^{3x} ?
The solution for y^{''}+2y^'+y=-e^{2x}+e^{3x} is y=c_{1}e^{-x}+c_{2}xe^{-x}-1/9 e^{2x}+1/16 e^{3x}