00:01
According to the question, given that y double dash minus 3y dash minus 4y is equal to 3e to part 2x, where y 0 is equal to 1 and y dash 0 is equal to 0.
00:20
Now we have to find out the differential equation using laplace transformation method.
00:38
So now according to the question, applying laplace.
00:48
Laplace transformation method to both of sides then we get l .y double dash is minus 3 l .y dash minus 4 ly is equal to 3l e to part 2x.
01:26
So now this is s square ly minus s y 0 minus y dash 0 minus 3 this is s ly minus y 0 minus 4 ly is equal to 3 divided by s minus 2 now this is equal to s square ly minus s into 1 multiplied with 1 minus 3 3 s ly plus 3 minus 4 ly is equal to 3 divided by s minus 2 this term is written in the form of s square minus 3 s minus 4 l y is equal to s minus 3 plus 3 divided by s minus 2 so now l s ly is equal to s minus 3 divided by s square minus 3, s minus 4, and plus 3 divided by s minus 2, s minus 4, s plus 1.
03:12
So now this is equal to s minus 3 divided by s plus 1, s minus 4, and this is 3 divided by s plus 1, s minus 4, and this is 3 divided by s minus 4, s minus 4, s plus 1 s minus 2 so this is equal to 1 divided by 4 5 s minus 4 plus 4 divided by 5 1 divided by s plus 1 minus 1 divided by 2 s minus 2 plus 1 divided by 5 s plus 1 plus 1 divided by 5 s plus 1 now, this is equal to 1 divided by 5 plus 3 divided by 10 and this is 1 divided by s minus 4...