Question: Show that the Midpoint method and the Modified Euler method give the same approximations to the initial-value problem y' = y + t + 1,

Show that the Midpoint method and the Modified Euler method give the same approximations to the initial-value problem
y' = −y + t + 1, 0 ≤ t ≤ 1, y(0) = 1,
For any choice of h. Why is this true?

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