56.3.1 problem Ex 1

Internal problem ID [14088]
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 : Thursday, October 02, 2025 at 09:11:31 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (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: 0.206 (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]
 

\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