78.8.2 problem 2

Internal problem ID [18129]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 2
Date solved : Monday, March 31, 2025 at 05:12:39 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (1-x y\right ) y^{\prime }&=y^{2} \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 17

ode:=(1-x*y(x))*diff(y(x),x) = y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 1.931 (sec). Leaf size: 25

ode=(1-x*y[x])*D[y[x],x]==y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.394 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x*y(x) + 1)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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