3. (Sec. 3.5) Consider the nonhomogeneous second order linear DE Ly] =y" +p(t)y' + g(t)y=g(t), where p, q, and g are continuous on an open interval I. Let Y₁ and Y₂ be two solutions of (1). (a) Show that Y₁ - Y₂ is a solution of L[y] = 0. (b) If y₁ and 2 form a set of fundamental solutions, then show that Y₁(t)-Y₂(t) = c(t) + 2/2 (t (1)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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8. (Sec. 3.5) Consider the nonhomogeneous second order linear DE
L[y] =y" +p(t)y' + q(t)y = g(t),
where p, q, and g are continuous on an open interval I. Let Y₁ and Y₂ be two solutions of (1).
(1)
(a) Show that Y₁ - Y₂ is a solution of Ly] =0.
(b) If y₁ and 2 form a set of fundamental solutions, then show that Y₁(t)-Y₂(t)=₁/(t) + 2/2 (t
Transcribed Image Text:8. (Sec. 3.5) Consider the nonhomogeneous second order linear DE L[y] =y" +p(t)y' + q(t)y = g(t), where p, q, and g are continuous on an open interval I. Let Y₁ and Y₂ be two solutions of (1). (1) (a) Show that Y₁ - Y₂ is a solution of Ly] =0. (b) If y₁ and 2 form a set of fundamental solutions, then show that Y₁(t)-Y₂(t)=₁/(t) + 2/2 (t
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