00:01
So we have given here each tank holding 24 liter of brine solution.
00:05
So each holding 24 liter of brine solution and take a tank a at a rate of 6 liter per minute drained out to tank b at same rate.
00:36
Now let's say this is a tank first.
00:38
This is a tank a.
00:39
This is the xt function let's say.
00:42
So here is a 24 liter of brine solution and here is a condition x0 is equal to 3.
00:52
Now we have here that is we have to drain the solution to tank b.
01:01
So from here we can write that is this is the tank b.
01:05
So here this will be yt function and this is also contain 24 liter of brine solution and here is the condition y0 is equal to 5 and then it's drained out at 6 liter per minute.
01:26
So here this will be 8 liter per minute and here will be 2 liter per minute.
01:35
Now we derive for two differential equation for dx upon dt and dy by dt in matrix form.
01:45
So we let's say the system equation is x dash is equal to ax.
01:52
So from here we can write the x dash element is x dash and y dash.
01:59
We need to write this into matrix form.
02:02
So from here we can write that is minus x upon 24 2 upon 24 whole up and second element is 8 upon 24 minus 8 upon 24 and multiply with x and y.
02:23
Now let's say here we have our a matrix will be then that is minus 1 upon 3 1 upon 12 1 upon 3 and minus 1 upon.
02:39
So we need to find the eigenvalue...