50.20.6 problem 4

Internal problem ID [8134]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.5. More on Regular Singular Points. Page 183
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:44:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 36

Order:=8; 
dsolve((x-1)^2*diff(y(x),x$2)-3*(x-1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=1);
 

\[ y = \left (x -1\right )^{2} \left (c_{1} \left (x -1\right )^{-\sqrt {2}}+c_{2} \left (x -1\right )^{\sqrt {2}}\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 34

AsymptoticDSolveValue[(x-1)^2*D[y[x],{x,2}]-3*(x-1)*D[y[x],x]+2*y[x]==0,y[x],{x,1,"8"-1}]
 

\[ y(x)\to c_1 (x-1)^{2+\sqrt {2}}+c_2 (x-1)^{2-\sqrt {2}} \]