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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 6 y = 19 sin (3 x)

x^{^{''}} - 3 x^{^{'}} + 2 x = t^{2} e^{t}

(D^{3} - D) y = 4 e^{(- x)} + 3 e^{2} x

y^{^{''}} + 36 y = 60 sin (6 t)

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

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