73.25.1 problem 35.2 (a)

Internal problem ID [15709]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional Exercises. page 715
Problem number : 35.2 (a)
Date solved : Tuesday, January 28, 2025 at 08:05:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x -3\right )^{2} y^{\prime \prime }-2 \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: 0.001 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 28

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

\[ y(x)\to c_1 \left (1-\frac {x^2}{9}\right )+c_2 \left (x-\frac {x^2}{3}\right ) \]