What is the solution for (d^2x)/(dt^2)+4*(dx)/(dt)+8x=0 ?

The solution for (d^2x)/(dt^2)+4*(dx)/(dt)+8x=0 is x=e^{-2t}(c_{1}cos(2t)+c_{2}sin(2t))

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(d^2x)/(dt^2)+4*(dx)/(dt)+8x=0

\frac{d ^{2} x}{d t ^{2}} + 4 \cdot \frac{d x}{d t} + 8 x = 0

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 4 \cdot \frac{d x}{d t} + 8 x = 0

Solve linear ODE:

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

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

(4 D^{3} - 5 D) y = 0

y - y^{^{''}} = 0

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 3

2 y^{^{''}} - 4 y^{^{'}} - 5 y = 0

y^{^{''}} + 9 y = 0, y^{^{'}} (0) = 0

What is the solution for (d^2x)/(dt^2)+4*(dx)/(dt)+8x=0 ?
The solution for (d^2x)/(dt^2)+4*(dx)/(dt)+8x=0 is x=e^{-2t}(c_{1}cos(2t)+c_{2}sin(2t))