Solve the following initial value problems (ivp) using the modified euler’s method with a) the average derivative and b) the derivative at midpoint: 1. dy dx = 4y x , subject to: y(1) = 2 → y(x) = 2x 4 2. dy dx = −2y − x, subject to: y(0) = −1 → y(x) = 2 − 3e −x − 2x integrate over the interval x = [1, 3] for the first ivp and over x = [0, 3] for the second ivp using 4 and 5 intervals. you will use the given true solution to determine the absolute error of the methods.