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).