plz helppppppp me Respect Sir about Power series

(x-1)(x-4)^2 d^2y/dx^2 + (x-4) dy/dx + (x-1)y = 0

- Find the ordinary points and the singular points of the above differential equation.
- Classify each singular point you find in 1. as a regular singular point or an irregular singular point.
- It is desired to solve this equation using a power series centered at 7. Find the radius of convergence of such a power series. (It is not required to find this power series solution!)

Re: plz helppppppp me Respect Sir about Power series

Do you know the **definitions** of "ordinary point" and "singular point"? Do you know what is meant by "regular" and "irregular" singular points? If not the first thing you should do is look them up in your text book!

You are asked to "Find the radius of convergence of a power series centered at 7". What does such a power series look like? What is the shortest distance from 7 to one of the singular points?