# Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations Academic Article

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### abstract

• We consider a 2 2 -dimensional system of linear ordinary differential equations whose coefficients are definable in an o-minimal

structure R \mathcal {R} . We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of R \mathcal {R} by all solutions at 0 of the system is o-minimal. We also show that if the coefficients of the system have a Taylor development of sufficiently large finite order, then the question of which of the two cases holds can be effectively determined in terms of the coefficients of this Taylor development.

• July 1, 2013