Let F(t, y) = t 2 y and let y(t) be the solution of dy/dt =
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Let F(t, y) = t2 − y and let y(t) be the solution of dy/dt = F(t, y) satisfying y(2) = 3. Let h = 0.1 be the time step in Euler’s Method, and set y0 = y(2) = 3.
(a) Calculate y1 = y0 + hF(2, 3).
(b) Calculate y2 = y1 + hF(2.1, y1).
(c) Calculate y3 = y2 + hF(2.2, y2) and continue computing y4, y5, and y6.
(d) Find approximations to y(2.2) and y(2.5).
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