00:01
Okay, to solve this differential equation, we'll have to solve this polynomial equation plus 49 m squared plus 28m plus 4.
00:15
Okay, and they tell us that one of the solutions is y equals the cosine of 2x.
00:20
That means that one of the ms here is 2i, and if 2i is one of them, then also minus 2i is one of them.
00:32
Okay, because if you get 2i for m, then you know cosine 2x plus c1 cosine 2x plus c2 sine 2x would be one of the solutions.
00:44
Okay, so that means what i could do is synthetic division using these two things.
00:53
But let's make it easier.
00:55
So if 2i is a root, then m minus 2i is a factor and m plus 2i is a factor.
01:03
And if you multiply those together, that gives you m squared plus four.
01:06
So i'm just going to divide that whole thing by m squared plus four using long division.
01:16
And that'll get it down to a quadratic equation, which hopefully we can solve by factoring.
01:25
All right, what do you multiply m squared by to get 12 m to the fourth? you multiply it by 12m squared.
01:34
So now multiply this whole thing by 12m squared.
01:36
You get 12m to the fourth plus 48.
01:41
M squared...
