Consider following initial value problem: dy where k 0.01, a 70 and b 50 and the exact solution is y(t) 350 1- exp(-0.21)] /[7-5 exp-0.2t)]. a) Verify that this is the solution, by substituting into the original differential equation. b) Use the method of separation of variables, to derive the solution. c) Write a MATLAB code to numerically solve the initial value problem over the interval [0, 20] using Euler's method with a fixed sample period, A 0.5. Calculate the error curve for the following sample periods Δ1-0.5, 0.2 and 0.1. d) Repeat part a) using Heun's method and the Runge-Kutta method.

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