73.23.22 problem 33.5 (j)

Internal problem ID [15668]
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 : 33.5 (j)
Date solved : Tuesday, January 28, 2025 at 08:03:54 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

Order:=6; 
dsolve((x^2-2*x+2)*diff(y(x),x$2)+(1-x)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=1);
 

\[ y = \left (1+\frac {3 \left (x -1\right )^{2}}{2}+\frac {3 \left (x -1\right )^{4}}{8}\right ) y \left (1\right )+\left (x -1+\frac {2 \left (x -1\right )^{3}}{3}\right ) y^{\prime }\left (1\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

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

\[ y(x)\to c_1 \left (\frac {3}{8} (x-1)^4+\frac {3}{2} (x-1)^2+1\right )+c_2 \left (\frac {2}{3} (x-1)^3+x-1\right ) \]