What is the solution for y^{''}-y^'-6y=e^{(-x)} ?

The solution for y^{''}-y^'-6y=e^{(-x)} is y=c_{1}e^{3x}+c_{2}e^{-2x}-1/4 e^{-x}

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y^{''}-y^'-6y=e^{(-x)}

y^{^{''}} - y^{^{'}} - 6 y = e^{(- x)}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{1}{4} e^{- x}

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = e^{(- x)}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{1}{4} e^{- x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{1}{4} e^{- x}

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What is the solution for y^{''}-y^'-6y=e^{(-x)} ?
The solution for y^{''}-y^'-6y=e^{(-x)} is y=c_{1}e^{3x}+c_{2}e^{-2x}-1/4 e^{-x}