What is the solution for d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0 ?

The solution for d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0 is x=e^{-3t}(c_{1}cos(t)+c_{2}sin(t))

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d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0

\frac{d}{d t} (\frac{d x}{d t}) + \frac{d}{d t} (6 x) + 10 x = 0

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0 ?
The solution for d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0 is x=e^{-3t}(c_{1}cos(t)+c_{2}sin(t))