0:00
Hello students.
00:01
Let's discuss the questions.
00:03
Here we have to solve the hink equation and having the subject to the initial and boundary conditions.
00:09
So let this equation be equation 1.
00:14
This equation in equation 1 we will use separation method.
00:33
So let u is equal to x t.
00:37
So del u divided by 10 t is equal to x t is equal to.
00:41
To x t dash and del u squared divided by del t squared is equal to x t double xt double dash now from one x t dash is equal to two x double dash t so this can be written as x double dash divided by x is equal to t divided by two t two t two t let this be equal to minus p square.
01:28
So we can write x double dash divided by x is equal to minus p square and t dash divided by 2t is equal to minus p square.
01:42
Now projecting ahead we have this is equal to x double dash plus xp square is equal to 0.
01:58
So, its auxiliary equation ae is n squared plus p square is equal to 0.
02:10
This gives n is equal to plus minus pi.
02:14
So, px equation is equal to c1 cost px plus c2 sine px and its particular integral will be 0.
02:31
So x is equal to c1 cost px plus p2 prime px.
02:42
Similarly we'll find in the case of p which is equal to t -dash plus 2 t square is equal to 0.
02:54
Its auxiliary equation will be m plus 2 p square is equal to 0.
03:01
So m is equal to minus 2p squared.
03:06
So it's cf is equal to 3e to the power minus 2p squared t and particular integral is 0.
03:18
So t is equal to 3e to the power minus 2 p square t...