7.5.8 problem 8

Internal problem ID [112]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 8
Date solved : Saturday, March 29, 2025 at 04:32:20 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x^{2} y^{\prime }&=x y+x^{2} {\mathrm e}^{\frac {y}{x}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 15

ode:=x^2*diff(y(x),x) = x*y(x)+x^2*exp(y(x)/x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.342 (sec). Leaf size: 18

ode=x^2*D[y[x],x]==x*y[x]+x^2*Exp[y[x]/x]; 
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**2*exp(y(x)/x) + x**2*Derivative(y(x), x) - x*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded