87.6.8 problem 8

Internal problem ID [23325]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:37:10 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} {\mathrm e}^{\frac {y}{x}}-\frac {y}{x}+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=exp(y(x)/x)-y(x)/x+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 16

ode=Exp[y[x]/x]-y[x]/x+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x \log (\log (x)-c_1) \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded