If x1 = y and x2 = y , then the second order equation y + p(t)y + q(t)y = 0 (i)
Chapter 7, Problem 4(choose chapter or problem)
If x1 = y and x2 = y , then the second order equation y + p(t)y + q(t)y = 0 (i) corresponds to the system x 1 = x2, x 2 = 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 a nonzero constant. Hint: y(1) (t) and y(2) (t) must be linear combinations of x11(t) and x12(t).
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