00:01
It is given that dx by dt is equal to x square plus y square minus 1 and dy by dt is equal to 2xy.
00:10
So x square plus y square minus 1 is equal to 0 and 2xy is equal to 0.
00:15
So if x is equal to 0 then y is equal to plus minus 1 and if y is equal to 0 then x is equal to plus minus 1.
00:23
So the possible equilibrium points are 0 1 0 minus 1 1 0 and minus 1 0.
00:36
Now let f is equal to x square plus y square minus 1 and y is equal and g is equal to 2xy.
00:46
So jacobian matrix jxy is equal to fx fy gx gy which is equal to 2x 2y 2y 2x.
01:00
So jx ,y is equal to 2x 2y 2y 2x.
01:07
Now at point 0 ,1 j is equal to 0 2 2 0.
01:13
So the eigenvalues will be determinant of 0 minus lambda to 2 0 minus lambda.
01:21
This will be equal to 0.
01:23
So lambda square minus 4 is equal to 0 and lambda is equal to plus minus 2...