What is the solution for (d^2x)/(dt^2)+9(dx)/(dt)+8x=2t ?

The solution for (d^2x)/(dt^2)+9(dx)/(dt)+8x=2t is x=c_{1}e^{-t}+c_{2}e^{-8t}+t/4-9/32

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(d^2x)/(dt^2)+9(dx)/(dt)+8x=2t

\frac{d ^{2} x}{d t ^{2}} + 9 \frac{d x}{d t} + 8 x = 2 t

x = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{t}{4} - \frac{9}{32}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 9 \frac{d x}{d t} + 8 x = 2 t

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{t}{4} - \frac{9}{32}

x = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{t}{4} - \frac{9}{32}

What is the solution for (d^2x)/(dt^2)+9(dx)/(dt)+8x=2t ?
The solution for (d^2x)/(dt^2)+9(dx)/(dt)+8x=2t is x=c_{1}e^{-t}+c_{2}e^{-8t}+t/4-9/32