Internal problem ID [10844]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 40(b).
ODE order: 2.
ODE degree: 0.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {m x^{\prime \prime }-f \left (x^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(m*diff(x(t),t$2)=f(diff(x(t),t)),x(t), singsol=all)
\[ x \left (t \right ) = \int \operatorname {RootOf}\left (t -m \left (\int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_f} \right )}d \textit {\_f} \right )+c_{1} \right )d t +c_{2} \]
✓ Solution by Mathematica
Time used: 1.546 (sec). Leaf size: 39
DSolve[m*x''[t]==f[x'[t]],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \int _1^t\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\&\right ]\left [c_1+\frac {K[2]}{m}\right ]dK[2]+c_2 \\ \end{align*}