71.1.17 problem 31

Internal problem ID [14247]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 31
Date solved : Wednesday, March 05, 2025 at 10:41:18 PM
CAS classification : [_separable]

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

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

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

\[ y = c_{1} \sqrt {x} \]

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

ode=2*x*D[y[x],x]-y[x]==0; 
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: 0.126 (sec). Leaf size: 8

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

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