What is the solution for (d^2x)/(dt^2)+6*(dx)/(dt)+8x=2e^{-3t} ?

The solution for (d^2x)/(dt^2)+6*(dx)/(dt)+8x=2e^{-3t} is x=c_{1}e^{-2t}+c_{2}e^{-4t}-2e^{-3t}

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(d^2x)/(dt^2)+6*(dx)/(dt)+8x=2e^{-3t}

\frac{d ^{2} x}{d t ^{2}} + 6 \cdot \frac{d x}{d t} + 8 x = 2 e^{- 3 t}

x = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 6 \cdot \frac{d x}{d t} + 8 x = 2 e^{- 3 t}

Solve linear ODE:

x = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

x = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

y^{^{''''}} - y = 4 t + cos (t)

y^{^{''}} + 6 y^{^{'}} + 9 y = 50 e^{2 x}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x \cdot e^{2 x}

2 y^{^{''}} + 3 y^{^{'}} + y = e^{- 3 x}

y^{^{''}} - y^{^{'}} = - 6

What is the solution for (d^2x)/(dt^2)+6*(dx)/(dt)+8x=2e^{-3t} ?
The solution for (d^2x)/(dt^2)+6*(dx)/(dt)+8x=2e^{-3t} is x=c_{1}e^{-2t}+c_{2}e^{-4t}-2e^{-3t}