84.6.4 problem 3.12

Internal problem ID [22105]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Supplementary problems
Problem number : 3.12
Date solved : Thursday, October 02, 2025 at 08:25:00 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);
 

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

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

✓ Sympy. Time used: 0.055 (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)
 

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