Factorization of entire solutions of some algebraic differential equations

We investigate the factorization of entire solutions of the following algebraic differential equations:bn(z)finjn(f′)+bn−1(z)fin−1jn−1(f′)+⋯+b0(z)fi0j0(f′)=b(z),bn(z)fin(f′)jn+bn−1(z)fin−1(f′)jn−1+⋯+b0(z)fi0(f′)j0=b(z), where n∈Nn∈N is a natural number, is⩾0is⩾0, js⩾0js⩾0, is+js>0is+js>0(0⩽s⩽n)(0⩽s⩽n) are the integers, and bi(z)≢0bi(z)≢0(0⩽i⩽n)(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.