What is the solution for 1q^{''}+8q^'+1/(0.05)q=80t ?

The solution for 1q^{''}+8q^'+1/(0.05)q=80t is q(t)=e^{-4t}(c_{1}cos(2t)+c_{2}sin(2t))+4t-8/5

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1q^{''}+8q^'+1/(0.05)q=80t

1 q^{^{''}} + 8 q^{^{'}} + \frac{1}{0.05} q = 80 t

q (t) = e^{- 4 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 t - \frac{8}{5}

Solution steps

1 q^{''} (t) + 8 q^{'} (t) + \frac{1}{0.05} q (t) = 80 t

Solve linear ODE:

q (t) = e^{- 4 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 t - \frac{8}{5}

q (t) = e^{- 4 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 t - \frac{8}{5}

What is the solution for 1q^{''}+8q^'+1/(0.05)q=80t ?
The solution for 1q^{''}+8q^'+1/(0.05)q=80t is q(t)=e^{-4t}(c_{1}cos(2t)+c_{2}sin(2t))+4t-8/5