  We study SMT problems over the reals containing ordinary differential
equations. They are important for formal verification of realistic hybrid
systems and embedded software. We develop delta-complete algorithms for SMT
formulas that are purely existentially quantified, as well as exists-forall
formulas whose universal quantification is restricted to the time variables. We
demonstrate scalability of the algorithms, as implemented in our open-source
solver dReal, on SMT benchmarks with several hundred nonlinear ODEs and
variables.
