00:01
Given triple differential equation y'' ' plus 2y' ' minus y ' minus 2y is equal to sin x.
00:19
Now it will be y'' ' plus 2y' ' minus y ' minus 2y is equal to zero.
00:35
Then s'' ' plus 2s ' square minus s minus 2ys is equal to zero.
00:48
Then s'' ' plus 2s square minus s minus 2 is equal to zero.
00:55
Now by solving it we have s is equal to 1, minus 1 and minus.
01:05
So equation y of t is equal to ae to the power t plus be to the power minus t plus ce to the power minus 2t where y0 is equal to y '0 is equal to y''0 is equal to zero.
01:32
Now at y0 is equal to zero, yt will be what? zero is equal to ae to the power zero plus be to the power minus zero plus ce to the power minus zero.
01:48
By solving it we get a plus b plus c is equal to zero.
01:54
We will take it as equation one.
01:58
Now y '0 is equal to zero.
02:02
Then yt will be what? zero is equal to ae to the power t minus be to the power minus t minus 2ce to the power minus 2t.
02:28
When we put zero then we have zero is equal to a minus b minus 2c.
02:36
We will take it as equation two.
02:40
Now at y''0 is equal to zero then y''t will be what? zero is equal to a plus b plus 4c.
02:54
We will take it as equation three...