New Exploration Of The Growth Of Two Order Linear Differential Equations

In this paper, we mainly applied the theory and methods of the complex analysis to study the three kinds of growth properties of second order linear differential equations.Firstly,Th1:Let A(z) and B(z) be two linearly independent solutions of ω〞 + P(z)ω= 0,Where P(z) is a polynomial,and L(A)< L(B),Then every nonzero solutions of ?〞+A(z)?′+B(z)?= 0 is of infinite order.Th2:Let ω1(z) and ω2(z) be two linearly independent solutions of ω〞+P(z)ω=0,Where P(z) is a polynomial,let c ∈ C and for δ(b, ω1/ω2)= 0,let A = ω1-bω2,Then A(z) has no finite Borel exceptional values. In addition,Th3:Let A(z) and B(z) be for meromorphic function, let δ(∞, B)> 0 and p(B)> p(A),Thenevery nonzero solution of P(?〞)+AP(?〞)+BP(?)= 0 is of infinite order.