Prove that if F(2) is a function with a finite number of linearly independent derivatives, i.e., if F(n)(x), F(n-1)(x),..., F'(x), F(x) are linearly independ- ent functions, where n is a finite number, then F(z) consists only of such terms as a, x, ea, sin ax, cos ax, and combinations of such terms, where a is a constant and k is a positive integer. Hint. Set the linear combination of these functions equal to zero, i.e., set C₂F(n)(x) + C-1F(n-¹)(x) +...+C₁F'(x) + CoF(x) = 0, where the C's are not all zero, and then show, by Lesson 20, that the only functions F(x) that can satisfy this equation are those stated.