Solving a Class of N-Order Linear Differential Equations by the Recursive Relations and itʹʹs Algorithms in MATLAB

In many applied sciences, we find differential equations, which these equations are N-Order Linear differential equations and solutions relatively complex, therefore researchers have forced to use numerical methods, which are contained several errors, i.e. In analysis of computer algorithms, notably in analysis of quicksort and search trees; a number of physics and engineering applications, such as when solving Laplaceʹs equation in polar coordinates; and many other sciences. In this paper, we are using variable change method for the analytic solution a class of N-Order Linear differential equations in problem. Applying a variable change in the equation, then we get conditions where if an equation is also conditions, a simple analytical solution is obtained for it. Because this solution, an exact analytical solution can provide to us, we benefited from the solution of numerical linear differential equations.