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}

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

\frac{d}{d x} (a b^{2} - x^{2})

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\int 49 tan^{5} (x) sec^{4} (x) d x

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}