51.4.10 problem 10

Internal problem ID [10367]
Book : First order enumerated odes
Section : section 4. First order odes solved using series method
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:22:39 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {y}{x}&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 14

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

\[ y = \frac {c_1}{x}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 9

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

\[ y(x)\to \frac {c_1}{x} \]

✗ Sympy

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,hint="1st_power_series",x0=0,n=6)
 

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