The linear differential equation of higher order in the unit disc is considered.Let f be a solution of homogeneous linear differential equation of higher order,and a sufficient condition for f to belong to the weighted Dirichlet space D_{q} or tothe Bergman space L_{a}^{p}, respectively, is obtained; and a sufficient condition for fto be nonadmissible is also given. Let f be a solution of nonhomogeneous lineardifferential equation of higher order f^{k}+A_{k1}（z）f^{k1}+…+A_{0}（z）f=F（z）,where A_{j}（z）（j=0,…, k1）, F（z）（?）0 are analytic in the unit disc, and therelation between the growth order of f and the growth orders of A_{j}（j=0,…, k1）and F is obtained under different conditions.The algebraic differential equation f^{12}=a_{0}（z）（fa_{1}（z））^{2}f, where a_{0}（z） anda_{1}（z） are analytic functions in the unit disc, is also considered. Let f be a solutionof the upper algebraic differential equation, and a sufficient condition for f tobelong to the weighted Hardy space H_{q}^{∞}, where 2≤q≤∞, is given.
