Consider the differential equation (D) : 2i(t) -8e-(t) +5=0, x(0) = In(4) and the relation y(t)...

 

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Consider the differential equation (D) : 2i(t) -8e-(t) +5=0, x(0) = In(4) and the relation y(t) = e(t) - 3. 1. Show that y(t) satisfies the differential equation (D) : 2y(t)+5y(t)+7=0, y(0) = 1 if and only if (t) satisfies the differential equation (D). 2 marks 2. Find the backward solution of (D) and deduce the backward solution of (D). 3 marks 3. Is the solution of (D) convergent or divergent? Justify your answer. 2 marks 4. Determine the stationary solution of (D) and indicate whether it is stable or unstable. 2 marks Consider the differential equation (D) : 2i(t) -8e-(t) +5=0, x(0) = In(4) and the relation y(t) = e(t) - 3. 1. Show that y(t) satisfies the differential equation (D) : 2y(t)+5y(t)+7=0, y(0) = 1 if and only if (t) satisfies the differential equation (D). 2 marks 2. Find the backward solution of (D) and deduce the backward solution of (D). 3 marks 3. Is the solution of (D) convergent or divergent? Justify your answer. 2 marks 4. Determine the stationary solution of (D) and indicate whether it is stable or unstable. 2 marks

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To solve the given problem lets follow the steps Show that yt satisfies the differential equation D2 2t 5yt 7 0 y0 1 if and only if xt satisfies the d... View the full answer