(a) Find the solution of the problem y' = 2ty2 with y(0)=1 over the interval 0

(a) Find the solution of the problem y' = 2ty2 over the interval O S t 0.2 with y(0)=1 ii) iii) iv) Using Euler's method with h = 0.2 Using Heun's method with h = 0.2 Compare your results with the exact solution y(t) = 1/(1 -f) and find the percentage errors for the results obtained in (i) and (ii). Why is the solution of the Heun's method more accurate? (b) Consider the second order differential equation (i) Convert this into a system of first order differential equations. (ii) Verify that the function x(t) 3' + 8te-3' is the solution.