32.6.23 problem Exercise 12.23, page 103

Internal problem ID [5888]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.23, page 103
Date solved : Tuesday, March 04, 2025 at 11:52:46 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 4.398 (sec). Leaf size: 38

ode=x*D[y[x],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 \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