Solutions of some classes of second order non-linear ordinary differential equations (Q1812611)

The author generalizes the results of \textit{J. L. Reid} [Proc. Am. Math. Soc. 38, 532-536 (1973)] to include second-order nonlinear differential equations of \textit{E.Kamke} [Differentialgleichungen, see p. 581, Chelsea, New York, 1948], of Lane-Emden, of Thomas-Fermi, of Emden-Fowler [\textit{Ph. Rosenau}, Int. J. Non-Linear Mech. 19, No. 4, 303-308 (1984; Zbl 0562.34002)], and of Kostin [the author, J. Phys. A 20, No. 17, 5935-5938 (1987)], as special cases. The theorem is proved by the direct substitution method. Two special cases of the main theorem are stated. Twenty-one corollaries and three examples are also given.