Problem 1: (25%) Consider the following non-linear differential equation for v(t): v + 2.4v + 3v3 = 3000 v(0-) = 10.01 (0-) = 2 (a) What is the equilibrium (final value) of v(t)? (b) Find a straight line approximation for v for values of v in the neighborhood of the equilibrium value. (c) Substitute you straight line equation for v in the original differential equation to obtain a linear differential equation. (d) The equilibrium value of your linear differential equation should be the same as the equilibrium value for the original differential equation. Is this the case? (e) What are the eigenvalues of your linearized differential equation? Time constants?