3.24 How to find the indicial equation for an ODE?

For say Bessel ode of order zero:

eq:= x^2*diff(y(x),x$2)+x*diff(y(x),x)+x^2*y(x)=0; 
DEtools[indicialeq](eq,x,0,y(x)); 
          #x^2 = 0
 

The third argument above is the singularity point of interest. So we have two roots, both zero. These are now used for finding the power series solution \(y(x)\) if needed.

Another example, is Bessel of order 1

eq:= x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-1)*y(x)=0; 
DEtools[indicialeq](eq,x,0,y(x)); 
          #x^2-1 = 0