ad 1) you could use root and the derivative, as odesolve returns sort of a pseudo-functions (vector of points but implicit interpolation) from which you can take the derivative and use root on it. See attached.
ad 2) you can't. The "functions" you have are only valid for 400<=x<=1000, so you can't explore what happens if x approaches infinity (which would be necessary to prove that a horizontal asymptote exists). The best you can "prove" is that all available values Z(x) are smaller than Z(1000) - thats no prove for a limit of course.
To verify a horizontal asymptote you would need Z(x) in an analytical form, that means you will have to solve the DE manually or with the help of Laplace, if possible. Then you could take the limit x-->inf and see what happens.
No account yet? Create an account
Enter your E-mail address. We'll send you an e-mail with instructions to reset your password.
