81.4.16 problem 5-17

Internal problem ID [21530]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-17
Date solved : Thursday, October 02, 2025 at 07:46:56 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 81

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

\begin{align*} y &= \frac {x \ln \left (x \right )+c_1 x +\sqrt {x \left (\ln \left (x \right )^{2} x +2 \ln \left (x \right ) c_1 x +c_1^{2} x +4\right )}}{2 x} \\ y &= \frac {x \ln \left (x \right )+c_1 x -\sqrt {x \left (\ln \left (x \right )^{2} x +2 \ln \left (x \right ) c_1 x +c_1^{2} x +4\right )}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 1.231 (sec). Leaf size: 77

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

\begin{align*} y(x)&\to \frac {x \log (x)+c_1 x-\sqrt {x \left (4+x (\log (x)+c_1){}^2\right )}}{2 x}\\ y(x)&\to \frac {x \log (x)+c_1 x+\sqrt {x \left (4+x (\log (x)+c_1){}^2\right )}}{2 x} \end{align*}

✗ Sympy

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

Timed Out