What is the solution for (d^2x)/(dt^2)+(dx)/(dt)-6x=4e^{-2t} ?

The solution for (d^2x)/(dt^2)+(dx)/(dt)-6x=4e^{-2t} is x=c_{1}e^{2t}+c_{2}e^{-3t}-e^{-2t}

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(d^2x)/(dt^2)+(dx)/(dt)-6x=4e^{-2t}

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} - 6 x = 4 e^{- 2 t}

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} - 6 x = 4 e^{- 2 t}

Solve linear ODE:

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

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

What is the solution for (d^2x)/(dt^2)+(dx)/(dt)-6x=4e^{-2t} ?
The solution for (d^2x)/(dt^2)+(dx)/(dt)-6x=4e^{-2t} is x=c_{1}e^{2t}+c_{2}e^{-3t}-e^{-2t}