A procedure for solving autonomous AODEs
نویسنده
چکیده
Consider the field of rational functions Kpxq for a field K and let d dx be the usual derivative. Then Kpxq is a differential field. We call Kpxqtyu the ring of differential polynomials. Its elements are polynomials in y and the derivatives of y, i. e. Kpxqtyu Kpxqry, y1, y2, . . .s. An algebraic ordinary differential equation (AODE) is one of the form F px, y, y1, . . . , ypnqq 0 where F P Kpxqtyu and F is also a polynomial in x. The AODE is called autonomous if F P Ktyu, i. e. if the coefficients of F do not depend on the variable of differentiation x. For a given AODE we are interested in deciding whether it has rational or radical solutions and, in the affirmative case, determining all of them.
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