(c) Identify the recurrence relation satisfied by the coefficients Ck. Problem 1. (20 points) Solve for the coefficient with the highest index. For which values In this problem you will find a series solution of the differential of k does your recurrence relation hold? equation (2+x)y" - (1+x) y' + 3y=0 of centered at 0. (d) Find the first five terms of the general series solution of the differential equation above. (Hint: your answer should be in terms (a) Analyze singular points to determine an interval on which the of co and c1.) series solution must converge. (b) Let (e) Consider the above differential equation together with the y = [CK. initial values: K=0 y(0) = 4, y(0) = 3. Substitute this expression for y into the left side of the differential equation and simplify to write as a single summation. What must Find the first five terms of the series solution of the initial value this simplified left side be equal to? problem. Generated by @WeBWork, http://webwork.man.org. Mathematical Association of America