29.8.8 problem 213

Internal problem ID [4813]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 213
Date solved : Sunday, March 30, 2025 at 03:59:32 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

✓ Mathematica. Time used: 0.337 (sec). Leaf size: 18

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

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

✗ 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