50.1.33 problem 6

Internal problem ID [7805]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 6
Date solved : Wednesday, March 05, 2025 at 05:06:24 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 19

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

\[ y = -\frac {\operatorname {LambertW}\left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )}{x^{2}} \]

✓ Mathematica. Time used: 3.015 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.466 (sec). Leaf size: 14

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

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