Exact solutions of nonlinear differential equations using continued fractions

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r)'' + 2φ(r)'/r + αφ(r)p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ''(r) -2φ(r)'/r + αφ(r)2p+1 + λφ(r)4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method