I have a question statement like this:
Show that solution of
$ y'' + NK\frac{y'}{t_f-t} + NK^2\frac{y}{(t_f-t)^2}=0 $
is
$ y(t) = C_1(t-t_f) + C_2(t-t_f)^N $.
N, K and tf are constants.
C1 and C2 are arbitrary constants.
y(t) is defined in the interval [0,tf).
I can't find a way to solve this differential equation. Can you please guide me by showing me a starting point. Any idea will be appreciated.
(Note: I double checked that I correctly wrote the question statement.)