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From the ODE manual (https://www.ode-wiki.org/wiki/index.php?title=Manual:_All&printable=yes):

"ODE uses a first order semi-implicit integrator. The "semi implicit" means that some forces are calculated as though an implicit integrator is being used, and other forces are calculated as though the integrator is explicit. The constraint forces (applied to bodies to keep the constraints together) are implicit, and the "external" forces (applied by the user, and due to rotational effects) are explicit. Now, inaccuracy in implicit integrators is manifested as a reduction in energy - in other words the integrator damps the system for you. Inaccuracy in explicit integrators has the opposite effect - it increases the system energy. This is why systems simulated with explicit first order integrators can explode."

Searching for integrator in the manual turns up other tidbits regarding ODE's integration behavior.