Denote Eulers method solution of the initial-value problem using step size h = 0.1 by X a

Question:

Denote Euler’s method solution of the initial-value problem

d.x dt xt 1 + 2 x(1) = 2

using step size h = 0.1 by X_a(t), and that using h = 0.05 by X_b(t). Find the values of X_a(2) and X_b(2). Estimate the error in the value of Xb(2), and suggest a value of step size that would provide a value of X(2) accurate to 0.1%. Find the value of X(2) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X_a(2), X_b(2) and your final value of X(2).