81.5.4 problem 6-4

Internal problem ID [21542]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 6. Method of grouping. Page 96.
Problem number : 6-4
Date solved : Thursday, October 02, 2025 at 07:47:26 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 19

ode=( y[x]^2-x*y[x] )/(x*y[x]^2)+(x/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}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 8

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

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