New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points
A second order algebraic differential equation of degree n is given by an equation of the form \(\Phi (z,y,y',y'')=0,\) where \(\Phi\) is a polynomial with meromorphic coefficients. This paper is concerned with the problem whether the solutions of this equation are free of movable critical points. If \(\Phi\) is linear in y'', much is known about it; the author here presents what appears to be the only interesting results known for equations of higher degree in y''. Some of the results are based on findings by the French nineteenth-century mathematician Paul Appell.
second order algebraic differential equation
scientific article; zbMATH DE number 4004640
scientific article