Lazarus Fuchs′ Transformation for Solving Rational First-Order Differential Equations

The neglect for over 108 years of a useful method that L. Fuchs introduced in 1884 to solve rational first-order differential equations is easily explained. Namely, no one had formulated the method precisely and no one had pointed out its wide applicability. This paper removes both of these deficiencies. In particular, it motivates details through a carefully selected series of examples and thereby provides a suitable context so that readers can learn to use the procedure effectively. Experts in computer programming could adapt the technique as a basis for desirable additions to current systems of computer algebra.