62.3.1 problem Ex 1

Internal problem ID [12728]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 1
Date solved : Wednesday, March 05, 2025 at 08:20:04 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.317 (sec). Leaf size: 18

ode=(x*Exp[y[x]/x]+y[x])-x*D[y[x],x]==0; 
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