Write a Matlab function called euler_timestep that solve the IVP dy/dt = f(t,y), a≤t≤b, y(0)=α using Euler's timestepping method. The header should look like function y - euler_timestep (f,a,b,alpha,N)
where N is the number of intervals used, so that Δt = b-a/N. Note that the output should be an array that contains the evaluation of the solution at all time steps. Use this method to solve the IVP dy/dt = (sin(2t) - 2ty)/t², y(1)=2, t = [1,5]
with N = 10, 10², 10³, Call y0, y1, y2 the three results. Plot the three solutions with respect to t. On another figure, make a loglog plot of absolute error at t = 5 versus the number of intervals for all three methods on the same plot. To compute the exact solution use the matlab function dsolve Cody coursework might not recognize the function dsolve, compute it on Matlab and copy the expression on Cody. Comment on your results (using %): which method works best, which method works the worst? Why?