Internal problem ID [2129]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations.
page 43
Problem number: Problem 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {m v^{\prime }-m g +k v^{2}=0} \end {gather*} With initial conditions \begin {align*} [v \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 26
dsolve([m*diff(v(t),t)=m*g-k*v(t)^2,v(0) = 0],v(t), singsol=all)
\[ v \relax (t ) = \frac {\tanh \left (\frac {t \sqrt {m g k}}{m}\right ) \sqrt {m g k}}{k} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 39
DSolve[{m*v'[t]==m*g-k*v[t]^2,{v[0]==0}},v[t],t,IncludeSingularSolutions -> True]
\begin{align*} v(t)\to \frac {\sqrt {g} \sqrt {m} \tanh \left (\frac {\sqrt {g} \sqrt {k} t}{\sqrt {m}}\right )}{\sqrt {k}} \\ \end{align*}