00:01
Okay, so for this problem, let's go ahead and start off by replacing the ys with r's instead.
00:06
So y delo prime translates to r squared, y prime transforms into r, and y transforms into 1.
00:16
And here i don't see any obvious factoring.
00:19
So to factor, let's go ahead and use the quadratic formula.
00:22
So we'll have negative b, plus or minus the square root of b squared, minus 4 times a times c.
00:31
All divided by two times a.
00:34
We can simplify down.
00:36
We'll have negative 1 plus or minus the square root of negative 7, all divided by 2.
00:46
And we have negative 1 half plus or minus i root 7 divided by 2.
00:53
And so from this, we can actually build our solution.
00:56
So our solution's going to be for the form c1 cosine of root 7 divided by 2 plus c2, sine of root 7 divided by 2, divided by 2 all times e to the negative 1 half and we can plug in our initial value conditions to solve for c1 and c2 so our initial value conditions are that c1 or sorry that y of 0 and y prime of zero both equal to zero let's go ahead and plug in y of zero so we have zero equals to the exterior right here sorry there's an extra this exterior is going to go to one and then and this right here is going to go to, sorry, i forgot the x terms...