65.6.15 problem 15

Internal problem ID [15708]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:23:42 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y^{2}}{1-y x} \end{align*}

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

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

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

✓ Mathematica. Time used: 1.128 (sec). Leaf size: 25

ode=D[y[x],x]==y[x]^2/(1-x*y[x]); 
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: 0.222 (sec). Leaf size: 10

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

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