23.1.681 problem 676

Internal problem ID [5288]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 676
Date solved : Tuesday, September 30, 2025 at 12:07:25 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 34

ode:=x*(1-x*y(x))^2*diff(y(x),x)+(1+x^2*y(x)^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{2 \textit {\_Z}}-2 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+2 c_1 \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 25

ode=x(1-x y[x])^2 D[y[x],x]+(1+x^2 y[x]^2)y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.735 (sec). Leaf size: 26

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

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