What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+5x=0 ?

The solution for (d^2x)/(dt^2)+4(dx)/(dt)+5x=0 is x=e^{-2t}(c_{1}cos(t)+c_{2}sin(t))

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(d^2x)/(dt^2)+4(dx)/(dt)+5x=0

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0

Solve linear ODE:

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

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

y^{^{''}} - 441 y = 0

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 10 x = 0

y^{^{'''}} + 2 y^{^{''}} + 4 y^{^{'}} + 8 y = 0

y^{^{''}} + y = 0, y (0) = 1

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = - 2, y^{^{'}} (0) = 5

What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+5x=0 ?
The solution for (d^2x)/(dt^2)+4(dx)/(dt)+5x=0 is x=e^{-2t}(c_{1}cos(t)+c_{2}sin(t))