44.17.17 problem 2(c) solving using series

Internal problem ID [9374]
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(c) solving using series
Date solved : Tuesday, September 30, 2025 at 06:17:56 PM
CAS classification : [_linear]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 24

Order:=8; 
ode:=diff(y(x),x)-y(x)/x = x^2; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 x \left (1+\operatorname {O}\left (x^{8}\right )\right )+x^{3} \left (\frac {1}{2}+\operatorname {O}\left (x^{5}\right )\right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 15

ode=D[y[x],x]-1/x*y[x]==x^2; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to \frac {x^3}{2}+c_1 x \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + Derivative(y(x), x) - y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=8)
 

ValueError : ODE -x**2 + Derivative(y(x), x) - y(x)/x does not match hint 1st_power_series