(a) Use Eulers method with step size 0.2 to estimate y (0.4), where y(x) is the solution...

Question:

(a) Use Euler’s method with step size 0.2 to estimate y (0.4), where y(x) is the solution of the initial-value problem y' = 2xy2 y (0) = 1
(b) Repeat part (a) with step size 0.1.
(c) Find the exact solution of the differential equation and compare the value at 0.4 with the approximations in parts (a) and (b).