Question: . Problem 3. Let a * 0 and A := -a2. Let dj, d2 6 R and define X : [0, (] -+ R as

. Problem 3. Let a * 0 and A := -a2. Let dj, d2 6 R and define X : [0, (] -+ R as X(x) := died+ doe or (x E [0, (]). (1) Show that X" + XX = 0. (2) Show, if X (0) = 0 and X'(() = 0, then di = d2 = 0. . Problem 4. Let a * 0 and A := 02. Let dj, d2 6 R and define X : [0, (] - R as X(x) := dj cos(or) + d2 sin(ox) (re [0, (]). (1) Show that X" + XX = 0. (2) Show, if X(0) = 0 and X'(@) = 0, then di = 0 and there exists some k E N so that of = ka - 1/2 and hence that (2k - 1)x O = 1

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