4. Consider the initial value problem y = x+y, y(0) = 1. (a) Use Euler's method with h = 0.1 to compute the approximate solutions yn y(In) at n nh for n = 1,2,3, that is, compute the approximate solutions y₁, 92, 93 at In = 0.1,0.2, 0.3, respectively. (b) Check that y(x) = 2e² - x - 1 is the analytical solution to the initial value problem. (c) Compute the error y(n)- yn at each rn; use the pre-calculated values of y(n) in the table; these were computed using the analytical solution y(r) using a calculator; do not re-compute these numbers yourself. Collect your results in the following table. n 0 1 2 3 In 0.0 0.1 0.2 0.3 Yn 1.00000 1.11034 1.24281 1.39972 y(xn) - Yn

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