6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).

Show that a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of the form y = m, where m is a constant if, and only if,m is a root of the second degree equation am² + bm + c = 0

9. (7.5) Find all exact solutions to the equation 2sin(30 ) + 1 = 0 on the interval [0, 2n).

Determine which of the following equations always valid (give an algebraic proof) are: (Q59) a'b + b'c + c'a = ab' + bc' + ca'