81.1.13 problem 2-12

Internal problem ID [21458]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-12
Date solved : Thursday, October 02, 2025 at 07:38:36 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = c_1 \,x^{2} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to c_1 x^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} x^{2} \]