5. Derive the improved Euler method with step size k for the following ODE d dty=y, y(0) = 1. Compare the numeric solution yn with the exact solution y(t) = et at t = nk. For fixed t≤ 1, show that if nk = t ≤ 1, n = £, we have y(t) - Yn → 0 if k→ 0. This implies that the numeric solution converges to the exact solution. You do not need to prove the convergence rate 0(²).

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A: NOTE:Kindly repost the other question as a separate question.

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A: NOTE: Refresh your page if you can't see any equations. .

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