00:01
Okay, we want to use laplace transforms to solve this equation given these initial conditions.
00:07
So we'll define capital y of s to be the laplace transform of little y of t.
00:13
So laplace transform of y prime is s times capital y.
00:18
And the laplace transform of y double prime is s squared times capital y.
00:23
Both of the initial conditions are zero, so there's no additional terms that come from it.
00:30
You substitute back into our equation.
00:35
We get an algebraic equation for capital y.
00:47
And we can see that the s plus 2 in the numerator there is going to cancel one of those.
00:57
So our capital y looks like this.
00:59
We have to separate it by partial fractions.
01:03
So we're looking for a, b, and c so that this is satisfied...