What is the solution for (d^2x)/(dt^2)=-k(dx)/(dt) ?

The solution for (d^2x)/(dt^2)=-k(dx)/(dt) is x=c_{1}+c_{2}e^{-kt}

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(d^2x)/(dt^2)=-k(dx)/(dt)

\frac{d ^{2} x}{d t ^{2}} = - k \frac{d x}{d t}

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} = - k \frac{d x}{d t}

Solve linear ODE:

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

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

x^{^{''}} + \frac{32}{2} x = 0, x (0) = - 1, x^{^{'}} (0) = - 2

x^{^{''}} + \frac{32}{2} x = 0, x (0) = - 1, x^{^{'}} (0) = - 5

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 8 y = 0

2 y^{^{''}} + 12 y^{^{'}} + 68 y = 0, y (0) = 3, y^{^{'}} (0) = 0

x^{^{'''}} + 7 x^{^{''}} - 5 x^{^{'}} - 75 x = 0

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