The integrability of an ordinary differential equation may refer to integration by quadratures (indefinite integrals); or to the existence of enough integrals of the system.
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Example Usage of Integrable
fernandotesta: Why the hell NEC build SIP phones that breaks RFC on purpose to a extent that they barely are Integrable in a heterogeneous environment?
math_book: A Memoir on Integrable Systems - by Yuri Fedorov et al. - Springer. http://tinyurl.com/yz6xvtv
science_book: A Memoir on Integrable Systems - by Yuri Fedorov et al. - Springer. http://tinyurl.com/yhp56dv