72.1.12 problem 1 (m)

Internal problem ID [19353]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (m)
Date solved : Thursday, October 02, 2025 at 04:19:24 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.258 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.288 (sec). Leaf size: 10

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

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