Finding the eigenvalues

Hello guys,

I have some system of differential equations,

How can i find  eigenvalues of this system?

If i have solution

res := evalf(dsolve(sys union ics, convert(x, list), type = numeric, method = rkf45))

and

sol := evalf(dsolve(sys union ics, convert(x, list), method = laplace))

AnSolution.mw

Thanks!