66.2.29 problem Problem 40(b)

Internal problem ID [13857]
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 : Monday, March 31, 2025 at 08:15:22 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 23

ode:=m*diff(diff(x(t),t),t) = f(diff(x(t),t)); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \int \operatorname {RootOf}\left (t -m \int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_f} \right )}d \textit {\_f} +c_1 \right )d t +c_2 \]

✓ Mathematica. Time used: 1.548 (sec). Leaf size: 39

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
m = symbols("m") 
x = Function("x") 
f = Function("f") 
ode = Eq(m*Derivative(x(t), (t, 2)) - f(Derivative(x(t), t)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : 
No algorithms are implemented to solve equation _Dummy_37*m - f(_X0)