73.23.6 problem 33.3 (f)

Internal problem ID [15652]
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 (f)
Date solved : Tuesday, January 28, 2025 at 08:03:40 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

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

\[ y = \left (x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 21

AsymptoticDSolveValue[D[y[x],x]+1/(x-1)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (x^5+x^4+x^3+x^2+x+1\right ) \]