Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem Question list K below. y'"' - vx+ 1y = sin x, y(n) = 9, y'(n) = 5, y"(1)= -9 O Question 1 O Question 2 (Type your answer in interval notation.)Question list 0 Question 1 0 Question 2 0 Question 3 0 Question 4 l Determine whether the given functions are linearly dependent or linearly independent on the specied interval. Justify your decision. {x6.x-1.6}on{m.m) Select the correct choice below and. if necessary. fill in the answer box to complete your choice. DA. DE. The functions are linearly dependent because cixs + c2 [x6 - 1] + c3(6] = E] has the solution c1: and c2 = 1. and c3 = (Type integers or simplied fractions.) The functions are linearly independent because clxs + c2 [x5 1) + c3(5) = E] has no solutions for constants c1. c2. and c3 that are not all zero. Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. Question list K {ex e2x, ex } on ( - 00,00) O Question 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O Question 2 A. The functions are linearly dependent because ce* + Cze + cy e = 0 has the solution C1 =|. C2 = , and C3 = - 1. (Type integers or simplified fractions.) O Question 3 B. The functions are linearly independent because ce + cze"+ Cge =0 has no solutions for constants Cy, C2, and c3 that are not all zero