29.17.3 problem 462

Internal problem ID [5060]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 462
Date solved : Sunday, March 30, 2025 at 06:34:16 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: 0.016 (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: 4.432 (sec). Leaf size: 33

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^{-1-\frac {c_1}{2}} x\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.639 (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)
 

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