84.13.3 problem 7.4

Internal problem ID [22153]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Solved problems. Page 29
Problem number : 7.4
Date solved : Thursday, October 02, 2025 at 08:32:49 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.061 (sec). Leaf size: 81

ode:=y(x)-x*y(x)^2+(x+x^2*y(x)^2)*diff(y(x),x) = 0; 
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: 0.819 (sec). Leaf size: 77

ode=(y[x]-x*y[x]^2)+(x+x^2*y[x]^2)*D[y[x],x]==0; 
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),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out