(1 point) In this exercise we consider finding the general solution of the first order linear equation y -2xy series solution in the form 0 This equation has an ordinary point at z 0 and therefore has a power y=Σ@nz We learned how to easily solve problems like this in several different ways 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 an 2for n = 1,2,⦠NOTE that a is an arbitrary constant and a1 using only the even terms as 0. The recurrence relation then implies that a2k- = 0 for k 0, 1, 2, . . . . Thus we see that the solution series can be written k 0 (2) Use the recurrence relation to find the first few coefficients in terms of ao ao (3) Write out a few more terms if needed but try to guess the pattern for the general term a0 for all k =1,2, (4) Therefore the general solution, with arbitrary constant ao can be written as 2k k 0 Notice The general solution of this first order linear equation is y = agez