- #1

member 731016

- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For this problem,

My solution is to find the characteristic equation of the system by putting the system into a matrix. This gives ##\lambda^2 + 2f \lambda + f^2 + 1 = 0##

Then each eigenvalue is ##\lambda_1 = -f - i## and ##\lambda_2 = -f + i##

I then want to find the Jacobian, however, I would need to find the partial derivatives (with respect to x and y) of ##F(x,y) = y - xf(x,y)## and ##G(x,y) = - x - yf(x,y)##, however, I'm not sure how to do that with the ##f(x,y)## in there.

Does anybody please know what I should do?

Thanks!

My solution is to find the characteristic equation of the system by putting the system into a matrix. This gives ##\lambda^2 + 2f \lambda + f^2 + 1 = 0##

Then each eigenvalue is ##\lambda_1 = -f - i## and ##\lambda_2 = -f + i##

I then want to find the Jacobian, however, I would need to find the partial derivatives (with respect to x and y) of ##F(x,y) = y - xf(x,y)## and ##G(x,y) = - x - yf(x,y)##, however, I'm not sure how to do that with the ##f(x,y)## in there.

Does anybody please know what I should do?

Thanks!