On meromorphic solutions of the Riccati differential equations
We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z)...