51.4.3 problem 3

Internal problem ID [10360]
Book : First order enumerated odes
Section : section 4. First order odes solved using series method
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 07:22:35 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✗ Maple

Order:=6; 
ode:=x*diff(y(x),x)+y(x) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*D[y[x],x]+y[x]==0; 
ic=y[0]==1; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

Not solved

✗ Sympy

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

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