What is the solution for x^{''}-x^'-6x=6e^{3t}+2e^{-2t} ?

The solution for x^{''}-x^'-6x=6e^{3t}+2e^{-2t} is x=c_{1}e^{3t}+c_{2}e^{-2t}+(6e^{3t}t-2e^{-2t}t)/5

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x^{''}-x^'-6x=6e^{3t}+2e^{-2t}

x^{^{''}} - x^{^{'}} - 6 x = 6 e^{3 t} + 2 e^{- 2 t}

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{6 e ^{3 t} t - 2 e ^{- 2 t} t}{5}

Solution steps

x^{''} (t) - x^{'} (t) - 6 x = 6 e^{3 t} + 2 e^{- 2 t}

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{6 e ^{3 t} t - 2 e ^{- 2 t} t}{5}

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} + \frac{6 e ^{3 t} t - 2 e ^{- 2 t} t}{5}

What is the solution for x^{''}-x^'-6x=6e^{3t}+2e^{-2t} ?
The solution for x^{''}-x^'-6x=6e^{3t}+2e^{-2t} is x=c_{1}e^{3t}+c_{2}e^{-2t}+(6e^{3t}t-2e^{-2t}t)/5