What is the solution for x^{''}-x^'-6x=2e^{4t} ?

The solution for x^{''}-x^'-6x=2e^{4t} is x=c_{1}e^{3t}+c_{2}e^{-2t}+1/3 e^{4t}

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x^{''}-x^'-6x=2e^{4t}

x^{^{''}} - x^{^{'}} - 6 x = 2 e^{4 t}

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

Solution steps

x^{''} (t) - x^{'} (t) - 6 x = 2 e^{4 t}

Solve linear ODE:

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

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

What is the solution for x^{''}-x^'-6x=2e^{4t} ?
The solution for x^{''}-x^'-6x=2e^{4t} is x=c_{1}e^{3t}+c_{2}e^{-2t}+1/3 e^{4t}