ODEPAINLEVE: a MACSYMA package for Painlevé analysis of ordinary differential equations. Nature of problem: Given a nonlinear ordinary differential equation, the program determines whether it fulfills certain necessary conditions for having the Painleve property, i.e. being free of moving critical points. This information is useful in attempts to integrate the ODE. Solution method: A truncated power series in t= x-xO’ where x is the independent variable y in the ODE. First only the leading term of the series is used in order to determine the negative rational value(s) of its exponent. Then for each such value the leading term and a generic term are used to locate possible resonances, i.e. indices of coefficients in the series which may be free parameters. Finally the full truncated series is used to verify these resonances.
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