(Solved): HW4: Problem 24 Previous Problem Problem List Next Problem (1 point) In this exercise we consider ...

HW4: Problem 24 Previous Problem Problem List Next Problem (1 point) In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (2+3) y' + 2y = 0 subject to the initial condition y(0) = 1. Since the equation has an ordinary point at 2 0 it has a power series solution in the form az y = 120 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 an = an-1 for n = 1,2, ... (2) Use the recurrence relation to find the first few coefficients ao 0 1 02= 03 (3) Write out a few more terms if needed and try to guess the pattern for the general term an = for all n 1,2,... (4) Therefore the solution can be written as y= 22 IM 9 Notice The general solution of this first order linear equation is y = (x+3)2