What is the solution for (dv)/(dt)=9.81-(0.5)/(v^{-1)} ?

The solution for (dv)/(dt)=9.81-(0.5)/(v^{-1)} is v=-2e^{(-t-c_{1})/2}+981/50

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(dv)/(dt)=9.81-(0.5)/(v^{-1)}

\frac{d v}{d t} = 9.81 - \frac{0.5}{v ^{- 1}}

v = - 2 e^{\frac{- t - c _{1}}{2}} + \frac{981}{50}

Solution steps

\frac{d v}{d t} = 9.81 - \frac{0.5}{v ^{- 1}}

Solve separable ODE:

v = - 2 e^{\frac{- t - c _{1}}{2}} + \frac{981}{50}

v = - 2 e^{\frac{- t - c _{1}}{2}} + \frac{981}{50}

What is the solution for (dv)/(dt)=9.81-(0.5)/(v^{-1)} ?
The solution for (dv)/(dt)=9.81-(0.5)/(v^{-1)} is v=-2e^{(-t-c_{1})/2}+981/50