常微分方程作業 Ch5-4.18 應數大二 洪美玲 0921959

Consider the nth order homogeneous linear differential equation Where a0,a1,...,an-1 are real constants. In each exercise, several function belonging to a fundamental set of solutions for this equation are given. (a) What is the smallest value n for which the given functions can belong to such a fundamental set? (b) What is the fundamental set? 答: (a) n = 8 (b) A fundamental set is { } 詳解: (a) 由 的根知, The characteristic equation is The characteristic equation is ∴ n = 8

詳解: (b)∵ The characteristic equation is Consider the nth order homogeneous linear different equation Where a0,a1,...,an-1 are real constants. In each exercise, several function belonging to a fundamental set of solutions for this equation are given. (a) What is the smallest value n for which the given functions can belong to such a fundamental set? (b) What is the fundamental set? 答: (a) n = 8 (b) A fundamental set is { } 詳解: (b)∵ The characteristic equation is 一般解 ∴ A fundamental set is { }