1. 常微分方程作業
Ch5-4.18
應數大二
洪美玲

2. 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

3. 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
{ }