Consider the differential equation (D₁) : 2x(t) — 8e¯ï(t) + 5 = 0, x(0) = ln(4)and the relation y(t) = e(t) — 3.1. Show that y(t) satisfies the differential equation (D₂): 2y(t)+5y(t)+7= 0,y(0) = 1 if and only if x(t) satisfies the differential equation (D₁).2. Find the backward solution of (D₂) and deduce the backward solution of(D₁).3. Is the solution of (D₁) convergent or divergent? Justify your answer.

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Answered: Consider the differential equation (D₁)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the differential equation (D₁) : 2ċ(t) — 8e¯ä(t) +5= 0, x(0) = ln(4) and the relation y(t) = eä(t) — 3. 1. Show that y(t) satisfies the differential equation (D₂) : 2ÿ(t)+5y(t)+7= 0, y(0) = 1 if and only if x(t) satisfies the differential equation (D₁).