Q1 (By hand & MATLAB/calculator, 15 pts) Consider the ordinary differential equation Į y' = -m [y2 – е-2t(t+ 1)] - -e-2t

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Q1 (By hand & MATLAB/calculator, 15 pts) Consider the ordinary differential equation Į y' = -m [y2 – е-2t(t+ 1)] - -e-2t (t2 + 1)?] – y + 2te-t y(0) = 1 whose true solution is y(t) = e-t(t2 +1) for all values of m. For [Q1], let m = 1 and step size h = 0.2, tk = kh (0 <k< N) (a) Evaluate yı = y(ti) obtained by the forward Euler's method. (b) Evaluate yi y(ti) obtained by the implicit trapezoid method (note that Crank- Nicolson in our textbook refers to the implicit midpoint method).