4.6.26 problem 26

Internal problem ID [1243]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 04:31:23 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 18

ode=x*D[y[x],x] == Exp[y[x]/x]*x+y[x]; 
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