00:01
Hello everyone, in this question it is given x dash equal to 1 3 2 2 x and x of 0 equal to 3 by 2.
00:08
So, we are here we have to solve this initial value problem.
00:11
So, we are we solve this by using x of t equal to e to the power a t x of 0.
00:17
So, first e to the power a t is nothing but i plus a t plus 1 by 2 factorial a square t square 1 by 3 factorial a cube t cube plus it goes on.
00:33
So, first a is given as 1 3 2 2.
00:38
So, a square if you multiply we will be having 7 9 6 8 and a cube will be a square into a that will give you 25 22 27 24.
00:51
So, in the next step we will substituting this in e to the power a t that is we will substitute values to e to the power.
01:00
Therefore, e to the power a t will be i plus 1 3 2 2 t plus 1 by 2 factorial 7 6 9 8 t square plus 1 by 3 factorial 25 22 27 24 t cube.
01:20
So, which is equal to 1 0 0 1 or we can directly write it as 1 0 0 1 plus t 2 t d t 2 t plus 1 by 2 factorial 7 t square 6 t square 9 t square 8 t square plus 1 by 3 factorial 25 t cube 22 t cube 27 t cube 24 t cube...