Written Homework 1 Math 207 1. a) Show that the function y = Csin (x ) solves the differential equation x- d'y_dy + 4x3y = 0, where C is dx2 dx any real-valued constant. b) Find C so that the function y = Csin (x2 ) solves the initial value problem (IVP) dx 2 dx d'y _dy + 4x y = 0, > VT - 6. 2. Consider the IVP = x-2y, y(1) =2 . Use Euler's Method to approximate the solution to the IVP at x = 3 dx by taking five steps. Make sure that you: ) Specify how each part of Euler's Method notation is defined in this problem. ii) Show how you set up each separate formula calculation step in Euler's Method. You may use a calculator to do the messy arithmetic calculations. ii) Give exact values of each y; (show all decimal places). iv) Write a concluding statement about the approximation using appropriate notation