1. (12 pts.) True/False and Short answer. For True/False questions, give a quick justification for your answer. (a) (3 pts.) True or False: The slope field below comes from an autonomous differential equation. 3.0 2.0 1.0 0.0 1.0 2.0 -3.0 -3 -2 -1 0 w (b) (3 pts.) True or False: If yo is an equilibrium point of the non-linear 2 x 2 system Y' = f(Y) and the Jacobian at yo has trace 2a" and determinant a for some real number a, then yo is an unstable equilibrium point. (c) (3 pts.) Find an integrating factor for ydx + (2xy - e-23) dy = 0. (d) (3 pts.) Suppose you are told the characteristic polynomial of a homogeneous linear differential equation with constant coefficients is given by p(x) = (x - 1)4(x2 + 1)3(x + 5). Write down the general solution to the differential equation