Sheet (1) (Ordinary Differential Equations) 1. Determine the order of the following differential equations and the degree: a. y` + xy = x2 b. (y``)3 + y` = x3 c. [ 1 + (y`)2 ] 3/2 = 4 y``` d. ( ) e. 2. Determine which of the following differential equations are Linear or non-Linear and study the Homogenous: a. x3 y``` - 4 x2 y`` + xy` + y = o b. x3 y`` + 2y` + y2 = 0 c. x10 y`` + (x2 + 1) y = 0 d. x3 y4 + ( 1 + x) y``` + sinx y + cosx = 0 e. x y``` y + y`` + ex y` + y = o 3. Find the particular solution of the differential equation: y`` = ex where, y`(1) = 0 & y(1) = 1 4. Show that the function y = A e3x + B e-3x is a solution to the differential equation: y``- 9y = 0, where A, B are arbitrary constants. 5. Show that the function y = A cosax + B sinax is a solution to the differential equation: y``+ a2y = 0, where A, B are arbitrary constants.