| Sumario: | Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second-order nonlinear ordinary differential equation ÿ + αf(y)ẏ + βf(y)(Latin small letter esh)f(y)dy + γf(y) = 0. Also, it appears in the generalized statistical mechanics for the most interesting value q = -1. The invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained. The linearization of that equation for any α, β, and γ is presented and for the important case f = byn + k with β = α2 (n + 1)/(n + 2)2 its explicit general solution is found. Moreover, the form invariance is applied to yield exact solutions of some other differential equations. © 1997 American Institute of Physics.
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