(a) Show that the ODE y + b'(x) y' - b(x) a b (x) = 0...

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(a) Show that the ODE y" + b'(x) y' - b(x) a b (x) = 0 has a pair of linearly independent solutions that are reciprocals (i.e., y(x) and (2)) where a is a constant and b(x) is a function of x. Find the two solutions in terms of a and b(x). (5 points) (b) If the ODE y" + p(x)y' + 2y = 0 has solutions y and y, find y and find p(x). There are two possibilities, find both. (5 points) (a) Show that the ODE y" + b'(x) y' - b(x) a b (x) = 0 has a pair of linearly independent solutions that are reciprocals (i.e., y(x) and (2)) where a is a constant and b(x) is a function of x. Find the two solutions in terms of a and b(x). (5 points) (b) If the ODE y" + p(x)y' + 2y = 0 has solutions y and y, find y and find p(x). There are two possibilities, find both. (5 points)