73.23.3 problem 33.3 (c)

Internal problem ID [15649]
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 (c)
Date solved : Tuesday, January 28, 2025 at 08:03:37 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {2 y}{2 x -1}&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

Order:=6; 
dsolve(diff(y(x),x)+2/(2*x-1)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 31

AsymptoticDSolveValue[D[y[x],x]+2/(2*x-1)*y[x]==0,y[x],{x,0,"6"-1}]
 

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