(a) Program a calculator or computer to use Euler's method to compute y(1) where y(x)is the solution of the initial-value problem
dy/dx + 3x2y = 6x2 y(0) = 3
(i) h = 1
(ii) h = 0.1
(iii) h = 0.01
(iv) h = 0.001
(b) Verify that y = 2 + e-x3 is is the exact solution of the differential equation.
(c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a). What happens to the error when the step size is divided by 10?