66.1.13 problem Problem 13

Internal problem ID [13789]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 13
Date solved : Monday, March 31, 2025 at 08:12:04 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=diff(x(t),t) = exp(x(t)/t)+x(t)/t; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \ln \left (-\frac {1}{\ln \left (t \right )+c_1}\right ) t \]

✓ Mathematica. Time used: 0.338 (sec). Leaf size: 18

ode=D[x[t],t]==Exp[x[t]/t]+x[t]/t; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -t \log (-\log (t)-c_1) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-exp(x(t)/t) + Derivative(x(t), t) - x(t)/t,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

RecursionError : maximum recursion depth exceeded