Part III: Extending the Ideas - Clearly write up Solutions and Explanations to this part for your group submission on Gradescope, due 4 days after your section meeting. In this part of the project we will see that the series technique for solving differential equations can be used to solve initial-value problems involving second order differential equations. (a) Let w > 0, and consider the initial-value problem dgy 2 ! = WY y(0) =1 '(0) = 0. Again, assume that the solution y(z) can be written as a Taylor series expanded about zero. he initial conditions will allow you to solve for ; and ;. Use the method of equating coeflicients, as we did in Part I and Part II to find the rest of the coefficients in the series that represents the solution. Show all of your work. (b) Use Maclaurin series to find the general solution to the differential equation y\" 2y' + y = 0. Then, write your general solution in a closed form (i.e., not using series)