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Given that dy/dt = y + et with y(0) = 0.
i) Apply Euler's Method to find ya (1) using step size h = 0.1;
ii) Apply Improved Euler's Method to find yb (1) using step size h = 0.1;
iii) Find the exact solution to the initial value problem;
iv) Estimate the errors in the predicted value of ya(1) and yb (1) and suggest a value of step size for each method that would provide a value of y(1) accurate to 0.5%.
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