00:01
In this question, we have the differential equation, y double prime minus y equals zero.
00:08
And we have to solve and find the particular solution.
00:12
So let's go ahead and assume that this solution has the form, y equals e to the kx.
00:23
So we're going to go ahead and write in our roots.
00:27
So we have y equals the root c, e to the x plus c2, c2, e to the negative x.
00:40
So this is assuming the roots are plus or minus one.
00:48
Our next step is to take the first derivative.
00:52
So we have y prime equals c1e to the x minus c2 e to the negative x.
01:03
Now we're going to use the initial condition that's given to us as y prime of 0 equals 0 and plug that in.
01:15
So we have 0 equals c1, e to the 0 is 1...