How to solve a second order linear homeogeneous ODE with Frobenius?

[fabsuk]

A simple question i think although i can't find in any books

What do u when u are solving a second order linear hoemoeneous differential equation with frobenius and there is no shift.

$$(X^2)(y^{''}) (-6y)=0$$ it should be normal minus -6y

I only know what to do if there is a shift.Help someone?

This is otherwise known as series solutions to differential equations

 

[fabsuk]

Does anybody know?

I keep trying but get nowhere i get an answer of 0 which i wrong.Help

 

[fabsuk]

Well i think i figured it out.
There is no recurrence relation and so your indical relations become your 2 values of the series.Thanks for the help.