51.4.5 problem 5

Internal problem ID [10362]
Book : First order enumerated odes
Section : section 4. First order odes solved using series method
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 07:22:36 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y&=1 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 11

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

\[ y(x)\to 1+\frac {c_1}{x} \]

✗ Sympy

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

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