On The Growth of Solutions of Second Order Linear Differential Equations

The growth of solutions of the differential equations $f''+A_{1}(z)P(e^z)f'+A_{0}(z)Q(e^z)f=0$ and $f''+(A_{1}P(e^z)+D_{1}(z))f'+(A_{0}Q(e^z)+D_{0}(z))f=0$ is investigated, where~$P(e^z)$~and~$Q(e^z)$~are nonconstant polynomials without constants, and deg$P$ is not equal to deg$Q$. It is showed that the order of growth of each nonzero solution of the above equations is infinite.