25.4.4 problem 3

Internal problem ID [6878]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 5
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 03:59:52 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y+\left (2 y-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 17

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

\[ y = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {x \,{\mathrm e}^{-\frac {c_1}{2}}}{2}\right )} \]

✓ Mathematica. Time used: 3.24 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to -\frac {x}{2 W\left (-\frac {1}{2} e^{-1-\frac {c_1}{2}} x\right )}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.395 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = e^{C_{1} + W\left (- \frac {x e^{- C_{1}}}{2}\right )} \]