Solution of a Class of High Order Differential Equations

In order to solve physical problems, we must establish mathematical models for the problems. Mathematical models often are differential equations relating an unknown function and one or more of its derivatives. In this paper, in order to solve high order differential equations, we first proved the expression for n repeated definite integrals by mathematical induction, Integration by parts and binomial formula. Then we obtained the solution of a class of high order differential equations by integral technique and the formula for n repeated definite integrals. Our results can be used to study the properties of high order differential equations, and then our results can be used to investigate physical or "real life" problems.