On certain non-linear differential equations in complex domains (Q998948)

Let \(M\) be a field of functions meromorphic in the complex plane \(C\). Consider meromorphic solutions of the ordinary differential equation over \(M\) \[ a_1y^2+a_2 (y')^2 = a_3 \tag{1.} \] In the previous paper (see [Arch. Math. 82, No.~5, 442--448 (2004; Zbl 1052.34083)]) the author has proved that if such solutions exist, then the equation (1) is reduced to the equation \[ y^2+a^2 (y')^2 = 1 \tag{2.} \] The full description of all meromorphic solutions for the equation (2) is given in the paper .