00:01
The first step to this problem is going to be rewriting our starting equation, which will be 2 plus 2 times e to the negative t.
00:11
You're rewriting 1 as e over e times the heavy side at 1 of t.
00:18
And when we do this, we can make a common factor inside of the parentheses here and remove the factor of e, 1 over e, to get that this is 2, plus 2 over e.
00:32
Times e to the negative t minus 1 minus e of the heavy side at 1 of t.
00:46
By doing this we can now, when we go to take the laplace transform, we're going to get the laplace transform of 2, which 2 is a constant.
00:56
So we can just pull it outside.
00:57
So this will be a laplace transformer of 1, but 1 is nothing other than t to the 0 with power, plus 2 over e times the laplace transform.
01:11
Of the heavy side at 1 of t times e to the negative t minus 1 minus the blanche transform of 2 over e times negative e will just be 2 negative 2 and then times the heavy side function at 1 and now we can look at each one of these individually so we can use our rules so we know that the plosh transform of t raises some integer n is just this so therefore this is cross -transform will be 2 times n is 0, so 0 factorial, and 0 factorial is just 1.
01:54
Over s to the 0 plus 1 is just 1 power, plus 2 over e times the plos transform of this...