Consider the differential equation (D₁) : 2ä(t) — 8e¯x(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) : 2ÿ(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).

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