Finding liouvillian solutions of first-order algebraic ordinary differential equations by change of variables
Abstract
We present an approach for determining liouvillian solutions of first-order algebraic ordinary differential equations (AODEs) by means of change of variables. In particular, a first-order AODE with liouvillian coeff icients can be transformed into an AODE over rational fields by the change of indeterminate over the ground fields. In addition, by the change of functions, the last AODE can be converted into the one which is suitable for known-algorithms. Some examples are given to illustrate the method.