50.17.13 problem 2(a) solving using series

Internal problem ID [8084]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 2(a) solving using series
Date solved : Sunday, March 30, 2025 at 12:44:58 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 12

Order:=8; 
ode:=x*diff(y(x),x) = y(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 x +O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 7

ode=x*D[y[x],x]==y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to c_1 x \]

✗ Sympy

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,hint="1st_power_series",x0=0,n=8)
 

ValueError : ODE x*Derivative(y(x), x) - y(x) does not match hint 1st_power_series