00:01
Hi, in this problem we have y double dash minus 2y dash plus 5y equal to 0.
00:10
So first we have to find the two linearly independent solutions for this.
00:17
So now the auxiliary equation is written as m square minus 2m plus 5 equal to 0, which implies that m is equal to 1 plus minus 2 aota.
00:37
So therefore the complementary function that is cf for this is equal to e power x into c1 cos to x plus c2 sine to x.
00:58
Therefore the two linearly independent solutions are given by y1 equal to e power x, cos 2x and y2 equal to e power x sine 2x.
01:17
Now next we have to find the value of the wrong skin for these two solutions such that these solutions are linearly independent.
01:27
Now the ron skin w for these two solutions is equal to determinant of y1 and y2, that is e power x, cost to x, e power x, sine to x, and derivative of y1 and y2, that is, e power x, cost 2x minus 2 e power x, sine to x, and e power x, sine to x plus 2e power x cost to x...