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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.)

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    they are not asking you to solve the differential equation. they are asking you to plug the putative y in and check that it is a solution.2012-12-19
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    @countinghaus Oh, I understand. I must only substitute y, y', y'' in to the differential equation and show that it could equal to zero with correct choices of C1 and C2. This way it will be much more easier.2012-12-19
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    hi hkBattousai, actually, it should be zero with ANY choice of C1 and C2, not just "a correct choice." But it should still be straightforward to check (the annoying part is keeping track which letters are constants).2012-12-19

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