Question: 4. (a) Show that {sin 1:, cos x} and {sin ac, sinx + cos x} are two distinct pairs of linearly independent solutions of y

4. (a) Show that {sin 1:, cos x} and {sin ac, sinx + cos x} are two distinct pairs of linearly independent solutions of y\" + y = 0. From this we can conclude that y1,y2 are not uniquely determined by an ODE in the form 31\" + P(-'L')3/ + Q(-'E)y = 0- (b) Show the functions P($) and Q(:z:) are uniquely determined by any pair of linearly independent solutions by the following, _ 3/1112\" 3123/1\" W(y1, 3/2) 91/92\" 92,91\" WW1, 2112) "U A H V II

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