73.23.4 problem 33.3 (d)

Internal problem ID [15650]
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 (d)
Date solved : Tuesday, January 28, 2025 at 08:03:38 AM
CAS classification : [_separable]

\begin{align*} \left (x -3\right ) y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

Order:=6; 
dsolve((x-3)*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {y \left (0\right ) \left (x -3\right )^{2}}{9} \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 20

AsymptoticDSolveValue[(x-3)*D[y[x],x]-2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^2}{9}-\frac {2 x}{3}+1\right ) \]