What is the solution for (d^2x)/(dt^2)-(dx)/(dt)-2x=4t ?

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

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(d^2x)/(dt^2)-(dx)/(dt)-2x=4t

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 4 t

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

Solution steps

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 4 t

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

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