. If x1 = y and x2 = y, then the second order equationy + p(t)y + q(t)y = 0

Chapter 7, Problem 4

(choose chapter or problem)

. If x1 = y and x2 = y, then the second order equationy + p(t)y + q(t)y = 0 (i)corresponds to the systemx1 = x2,x2 = q(t)x1 p(t)x2. (ii)Show that if x(1) and x(2) are a fundamental set of solutions of Eqs. (ii), and if y(1) and y(2)are a fundamental set of solutions of Eq. (i), then W[y(1), y(2)] = cW[x(1), x(2)], where c is anonzero constant.Hint: y(1)(t) and y(2)(t) must be linear combinations of x11(t) and x12(t).

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