![6. Consider the second-order scalar equation (2.19) with p,q,f continuous on an interval . Let ф, фг be linearly independent (a) Write (2.19) as an equivalent system of two first-order equations and show (scalar) solutions of the homogeneous equation associated with (2.19). that is a fundamental matrix of the associated homogeneous system on I. (b) Use Theorem 2.6 to find the solution ψ of the inhomogeneous system in part (a) for which ψ(fo)-.0, to on . (Or obtain this solution directly.) (c) Writing ψ . I , , show that W(«) f(s) ds t0 where W(t) , det Φ(1), is that solution of (2.19) for which ψΧο)-0, ψ(to)-0. (Compare with formula (3.34), p. 105 of [2]; where ao(t)s 1, ai(t)-p(t), a2(t)-q(t).)](https://media.cheggcdn.com/media%2F414%2F414de742-f63f-4fbb-8f43-4d4ae8d2df47%2Fphpw8jnCf.png)
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(Solved) : 6 Consider Second Order Scalar Equation 219 P Q F Continuous Interval Let Linearly Indepe Q32456569 . . . .
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