This approach identifies meromorphic solutions in algebraic differential equations, improving findings from previous studies by Li and Yang and Xu et al.
In the paper, we use the idea of normal family to find out the possible solution of the following special case of algebraic differential equation \[P_k(z,f,f⁽¹⁾,…, f⁽ᵏ⁾)=f⁽¹⁾(f-L_k(f))-φ(f-a)(f-b)=0,\] where Lₖ(f)=ᵢ₌₀ᵏ∑ aᵢ f⁽ⁱ⁾ and $φ$ is an entire function, aᵢ\;(i=0,1,…, k) such that aₖ=1 and a, b such that a≠ b. The obtained results improve and generalise the results of Li and Yang {LY1} and Xu et al. {XMD} in a large scale.
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Xu et al. (2025) studied this question.
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