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

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

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y^{''}-6y+y^'=e^x

y^{^{''}} - 6 y + y^{^{'}} = e^{x}

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

Solution steps

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

Solve linear ODE:

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

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

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