Using the Robertson-Walker metric, exact general solutions to the Brans-Dicke cosmologies for $p=\frac{1}{3}\rho$ are found. The two first integrals which exist for this case reduce the problem to quadratures. In the case of flat space the quadratures may be integrated explicitly in terms of elementary functions, while in the curved spaces ($k=\pm 1$), the solutions may be expressed in terms of elliptic integrals. The limit as $a$ approaches $\infty$ (or $a_{max}$ for a closed universe) may be evaluated for positive, negative, and zero curvature, and leads to the rather surprising result that the scalar field $\lambda$ approaches a constant.

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