00:01
Friends, we have to solve the equation by the laplace transformation.
00:07
So we can write it.
00:08
This they'll write d to y upon dt square plus 2 d, dy upon dt, thus y.
00:18
That is supposed to 3 into the power monastic.
00:21
Now we will take the laplace transform, taking laplace transform on both sides, both sides of the given equation.
00:51
So laplace transform of this will be s square y s minus s y of 0 minus y does 0 plus 2 into s y of s minus of y does 0 plus 2 into s y of s minus of y does 0 so this will be y 0 plus plus plus plus plus plus transform of y does y of s this will be equal to 3 into laplace transform of this will be 3 divided s plus 1 to the power of 2 so we will put the value of 0 and y -dus 2 so this will be y square y of s minus s y o 0 is 4 why does 0 is 2 plus 2 into s into y of s by of 0 is given 4 plus y of s that is equal 3 upon s plus 1 to the power of 2 so we can write it s squared into y of s minus 4 s minus 2 is 2 s y of s minus of 8 plus y of s that is equal to 3 divided by s minus plus 1 to the power of 2 we will take y s square plus 2 s plus 1 y s minus 4 s minus 2 minus 8 that is 3 divided by s plus 1 to the power of 2 so s square plus 2 s plus 1 y of s it is minus 4 s minus 10 that is divided by 3 s plus 1 to the power of 2.
04:04
So y of s that will be equal to 3 s plus 1 to the power of 2 plus 4 s plus 10.
04:18
S squared plus 2 is plus 1.
04:20
It will be like this.
04:22
So we can write y of s that is equals 3 upon s plus 1 square...
