84.13.6 problem 7.7

Internal problem ID [22156]
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 : 7.7
Date solved : Thursday, October 02, 2025 at 08:32:55 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 22

ode=D[y[x],x]==(x*y[x]^2-y[x])/x; 
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: 0.115 (sec). Leaf size: 10

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

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