81.5.5 problem 6-5

Internal problem ID [21543]
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 : 6-5
Date solved : Thursday, October 02, 2025 at 07:47:28 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 7

ode:=1/x*diff(y(x),x)-1/x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

ode=1/x *D[y[x],x]- y[x]/x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 5

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

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