20.1.5 problem Problem 11

Internal problem ID [3562]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 11
Date solved : Tuesday, March 04, 2025 at 04:50:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.094 (sec). Leaf size: 8

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

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