56.5.7 problem 7

Internal problem ID [8968]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 7
Date solved : Sunday, March 30, 2025 at 01:57:33 PM
CAS classification : [[_linear, `class A`]]

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

Using series method with expansion around

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 113

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

\[ y(x)\to \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \left (\frac {x^6}{2160}+\frac {x^5}{600}+\frac {x^4}{96}+\frac {x^3}{18}+\frac {x^2}{4}+x+\log (x)\right )+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]

✗ Sympy

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

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