Factorization of entire solutions of some algebraic differential equations

AbstractWe investigate the factorization of entire solutions of the following algebraic differential equations:bn(z)fin(f′)jn+bn−1(z)fin−1(f′)jn−1+⋯+b0(z)fi0(f′)j0=b(z), where n∈N is a natural number, is⩾0, js⩾0, is+js>0 (0⩽s⩽n) are the integers, and bi(z)≢0 (0⩽i⩽n) are the polynomials. Moreover, the results enable us to provide new criteria/proofs of primeness or pseudo-primeness for certain well-known classes of entire functions