'2. [20 pt] Solve the differential equation: 2:12:34 m+3 3%] = Identify the type of the equatinn and clearly ehew all steps; in solving it. 3. (30 pt) Consider the differential equation dy it # +1 a. Determine all equilibrium solutions, i.e. solutions of the form y(f) = (, where O is a constant. b. Sketch by hand the direction field for f > 0. c. Sketch by hand the graph of the solution of the IVP y(0) = 1 and compute lim, +x y(t) or state "does not exist".:1. [25 pt] Find a general eolution of the differential equation: if\") - y.) = it: cost Identify the type of the equation and clearly show all steps in solving it. 6. (25 pt) Solve the initial value problem y"(t) + 8y'(t) + 16y(t) = 0, y(0) = 3, y'(0) = -5 Identify the type of the equation and clearly show all steps in solving it.7. (25 pt) Use the method of undetermined coefficients to find a general solution to the differential equation: x" - 4r + 31 = -5et Identify the type of the equation and clearly show all steps in solving it