Winter 2022 MATH 201 Assignment 6 Due 11PM Friday 4 March 1. (10 points) Determine a recurrence relation for the coefcients in the power series about 3:0 = 0 for the general solution of (1 $2M\" +9' H; = mew- Use this to write the rst ve nonzero terms (i.e., all terms up to order x4 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 rst order differential equation 31' + xy = O with initial condition 00 y(1) = 1. Write the solution as a series y : Z ants 1)n expanded about cc : 1. Find n=0 the recurrence relation for the coefcients an and write the rst 4 nonzero terms. (b) (3 points) Solve this problem by earlier (Chapter 2) methods, using that this DE is either separable or linear. 3. (a) (5 points) Find all singular points in the complex plane for the equation 2(2 + $2)xy\" + my' + 3:823; = 0. (b) (5 points) If one attempts to solve the initial value problem 2(2 + $2M\" + y' + Bag = 0, 00 y(1) = 0, y'(1) = 1, by an expansion of the form y = Z an(:1: 1)\