I am opening this thread to expose some questions which are worth investigating. Any non-trivial question on differential equations is welcome.
To propose problems in other subjects, please use new threads. If some order is not followed the thread becomes useless. To expose those questions requiring complex formulae it is preferable to attach pdf files.
In http://www.emis.de/journals/SWJPAM/Vol2_2000/6.ps.gz it is proved that when iterating the vector X defining an autonomous system of differential equations, for some integer n, the function X^n X depends on the X, X^1X…X^(n-1) X, the system is equivalent to a linear one. The following is an open problem: If the infinite sequence X^1X, X^2X…. is independent, but X belongs to the vector space generated by them, can each solution be approached by solutions of linear systems?
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