00:01
Hello students, in this problem we are going to solve dx by dt is equal to x plus y.
00:10
Consider this as equation number one and dy by dt is equal to minus 2x minus y.
00:17
This is equation number two.
00:19
Now let us take x dash is equal to ax where x is equal to xy transpose.
00:30
So here a equal to 1 1 minus 2 minus 1 which is the coefficient matrix.
00:38
First we need to find eigenvalues.
00:41
For that we need to find characteristic equation and we know characteristic equation for 2 cross 2 matrix is lambda square minus s1 lambda plus s2 equal to 0.
00:59
Here s1 is equal to sum of the diagonals and that is equal to 1 minus 1 that is 0.
01:10
So s1 equal to 0 and s2 will be getting by taking the determinant of a.
01:16
So determinant a is equal to 1 1 minus 2 minus 1 which is equal to minus 1.
01:26
Therefore s2 equal to minus 1...