What is the solution for (d^2x)/(dt^2)+2(dx)/(dt)+4x=0 ?

The solution for (d^2x)/(dt^2)+2(dx)/(dt)+4x=0 is x=e^{-t}(c_{1}cos(sqrt(3)t)+c_{2}sin(sqrt(3)t))

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(d^2x)/(dt^2)+2(dx)/(dt)+4x=0

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 4 x = 0

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 4 x = 0

Solve linear ODE:

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

What is the solution for (d^2x)/(dt^2)+2(dx)/(dt)+4x=0 ?
The solution for (d^2x)/(dt^2)+2(dx)/(dt)+4x=0 is x=e^{-t}(c_{1}cos(sqrt(3)t)+c_{2}sin(sqrt(3)t))