LAZARUS FUCHS TRANSFORMATION FOR SOLVING RATIONAL 1ST-ORDER DIFFERENTIAL-EQUATIONS

The neglect for over 108 years of a useful method that L. Fuchs introd uced in 1884 to solve rational first-order differential equations is e asily explained. Namely, no one had formulated the method precisely an d no one had pointed out its wide applicability. This paper removes bo th of these deficiencies. In particular, it motivates details through a carefully selected series of examples and thereby provides a suitabl e context so that readers can learn to use the procedure effectively. Experts in computer programming could adapt the technique as a basis f or desirable additions to current systems of computer algebra. (C) 199 4 Academic Press, Inc.