8.5.8 problem 8

Internal problem ID [736]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 8
Date solved : Saturday, March 29, 2025 at 10:17:10 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

ode:=x^2*diff(y(x),x) = exp(y(x)/x)*x^2+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: 0.3 (sec). Leaf size: 18

ode=x^2*D[y[x],x] == Exp[y[x]/x]*x^2+x*y[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