67.23.7 problem 33.3 (g)

Internal problem ID [16940]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.3 (g)
Date solved : Thursday, October 02, 2025 at 01:40:32 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {y}{x -1}&=0 \end{align*}

Using series method with expansion around

\begin{align*} 3 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

Order:=6; 
ode:=diff(y(x),x)+1/(x-1)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=3);
 

\[ y = \left (\frac {5}{2}-\frac {x}{2}+\frac {\left (x -3\right )^{2}}{4}-\frac {\left (x -3\right )^{3}}{8}+\frac {\left (x -3\right )^{4}}{16}-\frac {\left (x -3\right )^{5}}{32}\right ) y \left (3\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 53

ode=D[y[x],x]+1/(x-1)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,3,5}]
 

\[ y(x)\to c_1 \left (-\frac {1}{32} (x-3)^5+\frac {1}{16} (x-3)^4-\frac {1}{8} (x-3)^3+\frac {1}{4} (x-3)^2+\frac {3-x}{2}+1\right ) \]

✓ Sympy. Time used: 0.165 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + y(x)/(x - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=3,n=6)
 

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