Question: how to make eigenvalues to be functions of time

I got the eigenvalues of the Jacobian matrix of a nonlinear time variant system. One of them is like: 0.5000000000e-2-0.2500000000e-2*y+0.5000000000e-2*x+0.2500000000e-2*sqrt(36.-12.*y-24.*x+y^2-4.*x*y+4.*x^2) Now I'd like to make x and y still vary with time, i.e. 0.5000000000e-2-0.2500000000e-2*y(t)+0.5000000000e-2*x(t)+0.2500000000e-2*sqrt(36.-12.*y-24.*x(t)+y(t)^2-4.*x(t)*y(t)+4.*x(t)^2) x(t) and y(t) bear a relation by differential equations. Any ideas on how I implement this? Thanks a lot!
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