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}

k = 0 \sum \infty 5 \cdot 3^{k}

- \frac{4 x}{( x ^{2} - 1 ) ^{2}}

x \to 0 + lim (x^{2} - 2 x - 3)

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))

y = \frac{5}{x}, (4, \frac{5}{2})

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