Please help!

Consider the following differential equation: (1 + x) dy dy + xy = 0, and the initial condition y(0) = 1. This equation is separable, but there are other techniques we can use to solve it as well. For example, we can try a series solution: y = [anan. 1=0 Here the unknown coefficients an of the power series are to be determined using the differential equation and the initial condition. 1. Use a power series solution to give the general solution of the differential equation above. Give a recursive formula for the coefficients an. Apply the boundary condition to find the solution such that y(0) = 1, and explicitly write out the first five non-zero terms of this series solution. 2. Solve the same problem by separation of variables. Find a power series representation of your solution (think Binomial Series) and write down the first five non-zero terms. Compare to your answer above