54.1.114 problem 117

Internal problem ID [11428]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 117
Date solved : Tuesday, September 30, 2025 at 08:20:31 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 3.941 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to x \log \left (\frac {1}{2} \left (-1+\tanh \left (\frac {1}{2} (-\log (x)-c_1)\right )\right )\right )\\ y(x)&\to i \pi x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(y(x)/x) + x*Derivative(y(x), x) - x - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded