00:01
Hi here for the given question.
00:03
We are given that here.
00:04
We have auxiliary equation as m multiplied with m plus 3 whole square multiplied with m square plus m plus 2 whole square is equal to 0.
00:15
So here for them we can write this as here.
00:19
We have value of m plus 3 equal to 0 m is equal to 0 which implies here.
00:26
We have e to the power 0 t which can be written as 1 for general solution.
00:31
So here we have m plus 3 is equal to 0.
00:34
So m is equal to minus 3 and it is whole square.
00:38
So repeated twice.
00:41
So here it can be written as e to the power minus 3.
00:45
Now further here we have m square plus m plus 2 is equal to 0.
00:52
So here m is equal to minus b plus or minus under root of b square minus 4 ac divided by 2a.
01:01
So substituting the values here we have minus 1 plus or minus under root of minus 7 divided by 2.
01:11
So here on simplifying further we have m is equal to minus 1 plus or minus under root 7 iota divided by 2...