Every nonconstant rational solution is of the form x=1/p(t), with S bounded by (n2-1)+2(n3-1) over C and by 12 over R under nondegeneracy.
Cano,An extension of the Newton–Puiseux polygon construction to give solutions of Pfaffian forms, Annales de l’Institut Fourier43(1) (1993), 125–142
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On the rational solutions of generalized Abel equations
Every nonconstant rational solution is of the form x=1/p(t), with S bounded by (n2-1)+2(n3-1) over C and by 12 over R under nondegeneracy.