1. (10 points) Determine a recurrence relation for the coefcients in the power series about .130 = 0 for the general solution of (1 - $2111\" + 11' +11 = mew - Use this to write the rst five nonzero terms (i.e., all terms up to order :34 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 3/ + my = 0 with initial condition a: y(1) = 1. Write the solution as a series 3; = 2 anti: I)\" expanded about 1' = 1. Find n=0 the recurrence relation for the coefcients on 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