00:03
Now, we have this second order linear with non -homogeneous term, and the non -homogeneous term is t to negative 1 power times exponential of t.
00:17
And in this problem, i mean, to this problem, we cannot, the method of undetermined coefficient would not work for this problem.
00:26
And the reason being that the homogeneous, non -homogeneous term here is, exponential times a non -polynomial here, basically.
00:41
This term here is what's given us trouble.
00:44
And the reason being that, so we can write it like this if you want.
00:51
And the whole idea of method of undetermined coefficient is that the right -hand side should be, let's call this f of t.
01:00
The whole idea is, now this is a bit non -rigorous, but the whole idea is that it should have finite finitely many derivatives.
01:23
Well, i should emphasize different derivatives, but this will work.
01:26
And you see that cosine sine, they only turn into each other, so there's only like two different derivatives.
01:35
Exponential just goes to itself.
01:38
So this is even nicer...