32.1.12 problem First order with homogeneous Coefficients. Exercise 7.13, page 61

Internal problem ID [5782]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.13, page 61
Date solved : Sunday, March 30, 2025 at 10:16:09 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.079 (sec). Leaf size: 15

ode:=x*exp(y(x)/x)+y(x) = x*diff(y(x),x); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.364 (sec). Leaf size: 15

ode=(x*Exp[y[x]/x]+y[x])==x*D[y[x],x]; 
ic=y[1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x \log (1-\log (x)) \]

✗ 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 = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded