81.4.1 problem 5-1

Internal problem ID [21515]
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 : 5-1
Date solved : Thursday, October 02, 2025 at 07:46:32 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {1}{\left (-\ln \left (x \right )+c_1 \right ) x} \]

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 10

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

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