20.6 problem 4

Internal problem ID [5713]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).

Solution by Maple

Time used: 0.023 (sec). Leaf size: 41

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);
 

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

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 34

AsymptoticDSolveValue[(x-1)^2*y''[x]-3*(x-1)*y'[x]+2*y[x]==0,y[x],{x,1,7}]
 

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