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

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Advance Math

(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!)

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