Internal problem ID [11672]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {m v^{\prime }-k v^{2}=-m g} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(m*diff(v(t),t)=-m*g+k*v(t)^2,v(t), singsol=all)
\[ v \left (t \right ) = -\frac {\tanh \left (\frac {\sqrt {m g k}\, \left (t +c_{1} \right )}{m}\right ) \sqrt {m g k}}{k} \]
✓ Solution by Mathematica
Time used: 14.167 (sec). Leaf size: 87
DSolve[m*v'[t]==-m*g+k*v[t]^2,v[t],t,IncludeSingularSolutions -> True]
\begin{align*} v(t)\to \frac {\sqrt {g} \sqrt {m} \tanh \left (\frac {\sqrt {g} \sqrt {k} (-t+c_1 m)}{\sqrt {m}}\right )}{\sqrt {k}} v(t)\to -\frac {\sqrt {g} \sqrt {m}}{\sqrt {k}} v(t)\to \frac {\sqrt {g} \sqrt {m}}{\sqrt {k}} \end{align*}