What is the solution for x^{''}-3x^'=e^{-3t} ?

The solution for x^{''}-3x^'=e^{-3t} is x=c_{1}e^{3t}+c_{2}+1/18 e^{-3t}

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x^{''}-3x^'=e^{-3t}

x^{^{''}} - 3 x^{^{'}} = e^{- 3 t}

x = c_{1} e^{3 t} + c_{2} + \frac{1}{18} e^{- 3 t}

Solution steps

x^{''} (t) - 3 x^{'} (t) = e^{- 3 t}

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} + \frac{1}{18} e^{- 3 t}

x = c_{1} e^{3 t} + c_{2} + \frac{1}{18} e^{- 3 t}

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What is the solution for x^{''}-3x^'=e^{-3t} ?
The solution for x^{''}-3x^'=e^{-3t} is x=c_{1}e^{3t}+c_{2}+1/18 e^{-3t}