What is the solution for y^{''}-9y=e^{-t}+1 ?

The solution for y^{''}-9y=e^{-t}+1 is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/8 e^{-t}-1/9

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y^{''}-9y=e^{-t}+1

y^{^{''}} - 9 y = e^{- t} + 1

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{8} e^{- t} - \frac{1}{9}

Solution steps

y^{''} (t) - 9 y = e^{- t} + 1

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{8} e^{- t} - \frac{1}{9}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{8} e^{- t} - \frac{1}{9}

\int (sec^{2} (x) - tan^{2} (x)) d x

\int_{- 7}^{7} (49 - x^{2}) d x

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\frac{d}{d x} (\frac{40}{0.01 x ^{2} + 1})

\frac{d}{d x} (e^{n x^{2}})

What is the solution for y^{''}-9y=e^{-t}+1 ?
The solution for y^{''}-9y=e^{-t}+1 is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/8 e^{-t}-1/9