Exercise 2 (35 points) Answer the following questions to numerically integrate (Euler's method): dy = f(x)=-3x3...

 

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Exercise 2 (35 points) Answer the following questions to numerically integrate (Euler's method): dy = f(x)=-3x3 +9x - 17x+1.5 dx from x = 0 to x = 1.8 with a step size of 0.6 the initial condition at x 0 is y = 1. a) Find the true solution y of the above equation. b) Use two steps: for each step compute the true solution ytrue and the Euler solution yEuler. c) Find the true error Et and the percent relative error &, for each step. Exercise 2 (35 points) Answer the following questions to numerically integrate (Euler's method): dy = f(x)=-3x3 +9x - 17x+1.5 dx from x = 0 to x = 1.8 with a step size of 0.6 the initial condition at x 0 is y = 1. a) Find the true solution y of the above equation. b) Use two steps: for each step compute the true solution ytrue and the Euler solution yEuler. c) Find the true error Et and the percent relative error &, for each step.