31.2.5 problem 5

Internal problem ID [5726]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 5
Date solved : Sunday, March 30, 2025 at 10:06:17 AM
CAS classification : [[_homogeneous, `class A`], _exact, _dAlembert]

\begin{align*} 1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 20

ode:=1+exp(x/y(x))+exp(x/y(x))*(1-x/y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 1.308 (sec). Leaf size: 34

ode=(1+Exp[x/y[x]])+Exp[x/y[x]]*(1-x/y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x/y(x) + 1)*exp(x/y(x))*Derivative(y(x), x) + exp(x/y(x)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded