In Exercises 13 40, evaluate the expression. Assume x 0.a) 45 42 b) (-4)5 (-4)2

Constant Coe¢ cient Homogeneeous DE. Case 1: Starting simple: Finding two Linearly independent solutions of Linear second order Constant Homogeneous DE s. Solutions to ▯ 2 ▯ 00 0 Ly = aD + bD + c y = ay + by + cy = 0: (1) Lets look at the simpler case of ▯ 2 ▯ 00 0 Ly = D + a D + 1 2 y = y + a y1+ a y 2 0: (2) 00 where the coe¢ cient of y is 1: To solve the homogeneous equation 00 0