What is the solution for x^{''}+5x^'+4x=t+1 ?

The solution for x^{''}+5x^'+4x=t+1 is x=c_{1}e^{-t}+c_{2}e^{-4t}+t/4-1/16

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x^{''}+5x^'+4x=t+1

x^{^{''}} + 5 x^{^{'}} + 4 x = t + 1

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{1}{16}

Solution steps

x^{''} (t) + 5 x^{'} (t) + 4 x = t + 1

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{1}{16}

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{1}{16}

What is the solution for x^{''}+5x^'+4x=t+1 ?
The solution for x^{''}+5x^'+4x=t+1 is x=c_{1}e^{-t}+c_{2}e^{-4t}+t/4-1/16