(1 point) In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem ly-xy + 2y = 0 subject to the initial condition y(0) = 1, y(0) = 3 Since the equation has an ordinary point at x 0 it has a power series solution in the form n=0 We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into the differential equation and derive the recurrence relation 2 Cr-2 for n = 2, 3, Cn The solution to this initial value problem can be written in the form y x = coy, x + cly(x) where co and Cl are determined from the initial conditions. The function y1 (x) is an even function and y2 (r) is an odd function For this example, from the initial conditions, we have co1 The function y2 (x) is an infinite series y2 (x) = x + Σ akX2kti and C1-3 (2) Use the recurrence relation to find the first few coefficients of the infinite series NOTE note that the constant ci has been factored out The function yl (x) is an even degree polynomial y = other words, note that the constant co has been factored out NOTE In the function y1 (r) the first term is 1. In