22.1.8 problem 8

Internal problem ID [4314]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 07:17:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }+\frac {x}{y}+2&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 21

ode:=diff(y(x),x)+x/y(x)+2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 31

ode=D[y[x],x]+x/y[x]+2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded