23.1.475 problem 465

Internal problem ID [5082]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 465
Date solved : Tuesday, September 30, 2025 at 11:34:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 17

ode:=(x-2*y(x))*diff(y(x),x) = y(x); 
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: 3.205 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.382 (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)
 

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