Q1) Solve the following initial value problem over the interval from 1= 0 to 2 where y(0) = 1. Display all your results on the same graph. dy yr² – 1.ly dt (a) Analytically. (b) Euler's method with h = 0.5 and 0.25. (c) Midpoint method with h = 0.5. Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. dy = (1 + 41) Vỹ dt (b) Euler's method. (c) Heun's method without iteration. (d) Ralston's method. (e) Fourth-order RK method.

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