What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+5x=0,x(0)=1 ?

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

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(d^2x)/(dt^2)+4(dx)/(dt)+5x=0,x(0)=1

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0, x (0) = 1

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

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

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