Relation between differential polynomials and small functions

In this article, we discuss the growth of solutions of the second-order nonhomogeneous linear differential equation where a, b are complex constants and A j ( z ) (cid:2)≡ 0 ( j = 0 , 1) , and F (cid:2)≡ 0 are entire functions such that max { ρ ( A j ) ( j = 0 , 1) ,ρ ( F ) } < 1 . We also investigate the relationship between small functions and differential polynomials g f ( z ) = d 2 f (cid:2)(cid:2) + d 1 f (cid:2) + d 0 f , where d 0 ( z ) ,d 1 ( z ) ,d 2 ( z ) are entire functions that are not all equal to zero with ρ ( d j ) < 1 ( j = 0 , 1 , 2) generated by solutions of the above equation.