00:01
Okay, we want to solve this equation.
00:04
I'm going to use laplace transforms.
00:06
We're given this initial condition.
00:11
So capital y of s is the laplace transform of y of t.
00:16
Laplace transform of the derivative is s times y.
00:21
Capital y, so there might normally be a term in there that involves the initial condition, but that's zero.
00:30
The laplace transform of that integral, that's a convolution integral.
00:35
So it's laplace transform of t times laplace transform of y.
00:42
Laplace transform of t is one over s squared.
00:45
Should be a square.
01:00
So we solve this equation for capital y...