88.6.7 problem 7

Internal problem ID [23989]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:49:31 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 60.1 (sec). Leaf size: 20

ode=D[y[x],{x,1}]==( x^2*Exp[y[x]/x]+y[x]^2 )/( x*y[x]  ); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x \left (1+W\left (\frac {\log (x)+c_1}{e}\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**2*exp(y(x)/x) + y(x)**2)/(x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : cannot determine truth value of Relational: -1 < x*exp(_X0/x)