Consider the IVP given by y''+y=0,y'(0)=0,y'(0)=1
(a) Write a recursive formula for the nth derivative of y for n>=2, i.e., write a formula for yⁿ in terms of lower order derivatives where n≥2. (d) Using the recursive formula found in part a),find a Maclaurin series that represents the solution to this ODE. (c) Find the solution to this ODE analytically and verify that it matches your expectation from the pre-vious part.
