81.4.14 problem 5-15

Internal problem ID [21528]
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 : 5-15
Date solved : Thursday, October 02, 2025 at 07:46:52 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = \frac {x}{x +c_1} \]

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {x}{x+e^{c_1}}\\ y(x)&\to 0\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 7

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

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