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

The solution for (d^2x)/(dt^2)+a*(dx)/(dt)=0 is x=c_{1}+c_{2}e^{-at}

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

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

x = c_{1} + c_{2} e^{- a t}

Solution steps

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

Solve linear ODE:

x = c_{1} + c_{2} e^{- a t}

x = c_{1} + c_{2} e^{- a t}

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

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 8

(d^{2} - 2) y = 0

\frac{d ^{6} y}{d x ^{6}} - 2 \frac{d ^{3} y}{d x ^{3}} + y = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = - 4, y^{^{'}} (0) = - 10

What is the solution for (d^2x)/(dt^2)+a*(dx)/(dt)=0 ?
The solution for (d^2x)/(dt^2)+a*(dx)/(dt)=0 is x=c_{1}+c_{2}e^{-at}