Davenport, James H. y’\(+fy=g\). (English) Zbl 0588.68013 EUROSAM 84, Symbolic and algebraic computation, Proc. int. Symp., Cambridge/Engl. 1984, Lect. Notes Comput. Sci. 174, 341-350 (1984). [For the entire collection see Zbl 0539.00015.] In this paper, we look closely at the equation of the title, originally considered by Risch, which arises in the integration of exponentials. We present a minor improvement of Risch’s original presentation, a generalisation of that presentation to algebraic functions f and g, and a new algorithm for the solution of this equation. Full details of the last two are to appear elsewhere. MSC: 68W30 Symbolic computation and algebraic computation 12H20 Abstract differential equations Keywords:solution algorithm; integration in finite terms; Risch differential equation; integration of exponentials; algebraic functions Citations:Zbl 0539.00015 PDFBibTeX XML