67.23.3 problem 33.3 (c)

Internal problem ID [16936]
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 : Thursday, October 02, 2025 at 01:40:30 PM
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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

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

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

ode=D[y[x],x]+2/(2*x-1)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.194 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 2*y(x)/(2*x - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

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