00:01
U -t -t is equal to uxx plus uyy.
00:06
Take this to be the first equation with a condition 0 less than x less than pi, 0 less than y less than pi, and t greater than 0.
00:18
Now consider u of x, y, t, is equal to x of x, y of y, and t, and t of t.
00:31
Therefore, equation 1 implies xy t double dash is equal to x double dash y t plus xy double dash t, which implies t double dash by t is equal to x double dash by x plus y double dash by y equal to k.
00:54
So if k value is less than 0 implies k is equal to minus lambda square, which implies t double dash by t is equal to x double dash divided by x plus y double dash divided by y equal to minus lambda square.
01:18
So then we will be having t double dash divided by t equal to minus lambda square.
01:25
T double dash plus lambda square t equal to 0 where t of t is equal to a cos lambda t plus b sine lambda t and the next concept is x double dash by x divided by x plus y double dash divided by y is equal to minus lambda square implies x double dash divided by x is equal to minus y double dash divided by y minus lambda square equal to p is a constant.
02:06
If p is less than zero, if p is less than zero implies p or minus l square.
02:18
P will be equal to minus l square...