67.3.31 problem 4.7 (e)

Internal problem ID [16352]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (e)
Date solved : Thursday, October 02, 2025 at 01:22:08 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 7

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

\[ y = c_1 x \]

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

ode=D[y[x],x]==y[x]/x; 
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: 0.056 (sec). Leaf size: 5

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

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