Exercise 1: In the notes, we have solved the following three SL problems [0, 1]: (SL1): y" (x) + Ay(x) =0, (SL2): y" (x ) + Ay(x) = 0, y(0) = y(1) = 0. y'(0) = y'(1) = 0. (SL3): y" (x) + dy(x) =0, y(0) = y'(1) =0. Using the notes, list all the eigenvalues and eigenfunctions for each problem. Note: You do not need to include the steps. This a chance for you to summarize the results of the derivations done in the notes. Exercise 2: Solve the following SL problem: (SL4): y" (x ) + dy(z) = 0, y'(0) = y(1) = 0. Note 1: This is similar to (SL3). Discuss the case A 0. Note 2: So far, we have solved the four basic SL problems on [0, 1]. We shall call them the fantastic four