66.2.29 problem Problem 40(b)

Internal problem ID [13928]
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)
Date solved : Tuesday, January 28, 2025 at 06:08:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} m x^{\prime \prime }&=f \left (x^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.033 (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: 1.548 (sec). Leaf size: 39

DSolve[m*D[x[t],{t,2}]==f[D[x[t],t]],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \int _1^t\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\&\right ]\left [c_1+\frac {K[2]}{m}\right ]dK[2]+c_2 \]