22.1.93 problem 115

Internal problem ID [4399]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 115
Date solved : Tuesday, September 30, 2025 at 07:27:44 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

✓ Mathematica. Time used: 0.225 (sec). Leaf size: 16

ode=x*D[y[x],x]== y[x]-x*Exp[y[x]/x]; 
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(x*exp(y(x)/x) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded