MATH 2255: Differential Equations Final Review Questions Prof. ll Final: 29-Jul The problems below should provide decent review for the various techniques to solve ODEs that we covered in this class. That being said, this is not to be taken to be an all inclusive list of all you need to know. You should be familiar with modeling (particularly spring-mass systems), how to determine constants so that initial conditions are satisfied if provided, numerical methods (particularly Euler's Method), and various aspects of the theory (Picard's theorem in all its forms, Wronskian, etc). Expect a potpourri problem on the final that deals with these aspects (similar to problem 4 from exam 3). (x + 2) sin y . 1. Find the general solution to y = x cos y 2. Find the general solution to y 2xy = 6xex 2 3. Find the general solution to xy = (1 2x2 ) tan x 4. Find the general solution to y 2y + 5y = sin(t) 5. Find the general solution to y (4) y = U (t 1) sin(t). 6. Find the general solution to y 3y + 2y = 1 . 1 + ex 7. Find the general solution to y + xy + y = 0 centered about the ordinary point x0 = 0. 8. Find the general solution to y + xy + y = x centered about the ordinary point x0 = 0. 9. Find the general solution to 2x2 y + xy (x + 1)y = 0 centered about the regular point x0 = 0