(Theorem 3.1): If xp is any solution of (∗) x′′ + p(t)x′ + q(t)x = f...

(Theorem 3.1): If xp is any solution of (∗) x′′ + p(t)x′ + q(t)x = f (t), and xh is a general solution of (∗∗) x′′ + p(t)x′ + q(t)x = 0), then the sum x = xh + xp is a general solution of (∗).

(a) First show that x = xp + xh satisfies (∗).

(b) Next show that if xp1 and xp2 are any two solution of (∗) then x = xp1 − xp2 satisfies (∗∗).

(c) Conclude that Thm 3.1 holds. (Explain your reasoning!)

Expert Solution

Colby Messinger answered 1 year ago

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