Winter 2022 MATH 201 Assignment 6 Due 11PM Friday 4 March 1. (10 points) Determine a recurrence relation for the coefficients in the power series about To = 0 for the general solution of (1 - x2 ) y" tyty= xe'. Use this to write the first five nonzero terms (i.e., all terms up to order a* inclusive) of the general solution. 2. Series solutions can be used to solve differential equations of any order, though this is not always the best method. (a) (7 points) Consider the first order differential equation y' + xy = 0 with initial condition y(1) = 1. Write the solution as a series y = _ an(x - 1)" expanded about r = 1. Find n=0 the recurrence relation for the coefficients an and write the first 4 nonzero terms. (b) (3 points) Solve this problem by earlier (Chapter 2) methods, using that this DE is either separable or linear