\[ v = -\hat{v} + (v_{0}+\hat{v})e^{- \gamma t} \tag{6.3.25}\label{eq:6.3.25} \] The second time integral (obtained by writing \( v\) as \( \frac{dy}{dt}\) in Equation \(\ref{eq:6.3.25}\)) and the spa...\[ v = -\hat{v} + (v_{0}+\hat{v})e^{- \gamma t} \tag{6.3.25}\label{eq:6.3.25} \] The second time integral (obtained by writing \( v\) as \( \frac{dy}{dt}\) in Equation \(\ref{eq:6.3.25}\)) and the space integral (obtained by writing \( \ddot{y} \) as \( v\frac{dv}{dy}\) in the equation of motion) require some patience, but the results are \[ v = v_{0} - \gamma y -\hat{v}\ln \left(\frac{\hat{v}+v_{0}}{\hat{v}+v}\right). \tag{6.3.28}\label{eq:6.3.28} \]
