00:01
We want to find the general solution of this differential equation, and you've got some stuff equal to the hyperbolic cosine of 2t.
00:08
So we want to switch it to something we know, so that's e to the 2t plus e to the minus 2t all over 2.
00:17
So i'm just going to put each one over 2.
00:20
All right, so next we have to solve this.
00:23
M squared minus m minus 2 equals 0.
00:27
So m minus 2, m plus 1.
00:31
M is 2 and m is negative 1 so y c is c1 e to the negative t plus c2 e to the 2 t all right then we're going to do undetermined coefficients so we're going to guess a e to the minus 2 t plus b e to the 2 t but that b e the 2t is a repeat of this, so we're going to have to put a t in there.
01:06
Okay, so then we need the first derivative, which would be minus 2a, e to the minus 2t, plus, now this is a product, so you can have to do the product rule, bt times 2e to the 2t, plus e to the 2t times b.
01:25
So minus 2a, e to the minus 2t, plus 2b, t, e to the 2t, plus b, t, each the 2t...