35.9.1 problem 1, using series method

Internal problem ID [6236]
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 : 1, using series method
Date solved : Sunday, March 30, 2025 at 10:44:19 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 35

Order:=6; 
ode:=x*diff(y(x),x) = x*y(x)+y(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 x \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 38

ode=x*D[y[x],x]==x*y[x]+y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 x \left (\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

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