00:04
Given that y double dash minus 4y dash is equal to 1 plus e power minus t.
00:13
So d square plus 4dy is equal to 1 plus e power minus t.
00:21
So the auxiliary equation is m square plus 4m equals to 0.
00:33
So m plus 4 equals to 0.
00:37
So there is m equals to 0 and minus 4.
00:42
So cf is equal to c1 e power 0t plus c2 e power minus 4t.
00:53
So cf is equal to c1 plus c2 e power minus 4t.
01:04
So we have to find pi.
01:07
So pi is equal to 1 plus e power minus t upon d square plus 4d.
01:15
So pi is equal to 1 upon d square plus 4d plus e power minus t upon d square plus 4d.
01:27
We know that 1 upon fd of e power ax is equal to 1 upon fa e power ax.
01:40
So pi is equal to 1 upon d square plus 4d plus e power minus t upon minus 1 square plus 4 minus 1.
02:02
So pi is equal to 1 upon d square plus 4d plus e power minus t upon 1 plus minus 4...