37. Suppose p and q are continuous on (a, b) and xo is in (a, b). Let yi and y2

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37. Suppose p and q are continuous on (a, b) and xo is in (a, b). Let yi and y2 be the solutions of y" + p(x)y' + q(x)y = 0 such that Theorem 5.1.1 implies that each of these initial value problems has a unique solution on (a, b)) (a) Show that {yi, y2) is linearly independent on (a, b). (b) Show that an arbitrary solution y of(A) on (a, b) can be written as y = y(xo)I +y'(xo)2. c Express the solution of the initial value problenm y', + p(x)y' + q(x)y = 0, of yi and y y(xo) = ko, y'(xo) = ki as a linear combination of yi and y2

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