Yang–Li's conjecture on meromorphic solutions of a polynomial differential equation

From papers

Let P1P_1, P2P_2 and P3P_3 be non-zero polynomials. Consider the differential equation

P1f2+P2(f(1))2=P3.P_1f^2+P_2(f^{(1)})^2=P_3.

Yang–Li's conjecture. The equation has no transcendental meromorphic solution when P1/P3P_1/P_3 is a non-zero constant and P2/P3P_2/P_3 is not the square of any rational function.

This conjecture concerns the existence of transcendental meromorphic solutions for a first-order nonlinear differential equation with polynomial coefficients. The supplied text gives no evidence that the conjecture has been resolved.

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Sources & referencesView supporting material

Primary source

Sujoy majumder, Nabadwip Sarkar and Debabrata pramanik, “Meromorphic solutions of a certain type of nonlinear differential equation”, arXiv:2512.15750 (2025).

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