67.5.18 problem 6.7 (f)

Internal problem ID [16416]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (f)
Date solved : Thursday, October 02, 2025 at 01:29:53 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y\right ) y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 13

ode:=(x+y(x))*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{\operatorname {LambertW}\left (x \,{\mathrm e}^{c_1}\right )} \]

✓ Mathematica. Time used: 2.604 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {x}{W\left (e^{-c_1} x\right )}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.328 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = e^{C_{1} + W\left (x e^{- C_{1}}\right )} \]