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

The solution for y^{''}-6y=e^x is y=c_{1}e^{sqrt(6)x}+c_{2}e^{-sqrt(6)x}-1/5 e^x

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

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

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{x}

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{x}

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 6} e^{5 t}

y^{^{''}} - y^{^{'}} - 2 y = x e^{4 x}

q^{^{''}} + 100 q^{^{'}} + 2500 q = 40, q (0) = 0

(D^{2} + 5) y = cos (5) x

(D^{2} + 4 D + 4) y = 5 e^{3 x}

What is the solution for y^{''}-6y=e^x ?
The solution for y^{''}-6y=e^x is y=c_{1}e^{sqrt(6)x}+c_{2}e^{-sqrt(6)x}-1/5 e^x