35.9.6 problem 3, using elementary method

Internal problem ID [6241]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 3, using elementary method
Date solved : Wednesday, March 05, 2025 at 12:27:15 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 7

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

\[ y = c_{1} x \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 14

ode=x*D[y[x],x]==y[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: 0.117 (sec). Leaf size: 5

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

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