Please explain how to solve the following questions and reference any rules, formulas, or tricks that apply.

6.1 1. Find the particular integral of each equation: (@) y"(t) - 2y'(1) + 5y = 2 (d) y" (t ) + 2y' (1) - y=-4 (b) y" (t ) + y (0) =7 (e) y"(0) = 12 (c) y"(!) + 3y=9 2. Find the complementary function of each equation: (@) y"(t) + 3y'(t)- 4y = 12 (() y"(!) - 2y'(0)+ y =3 (b) y" (t) + 6y'(t) + 5y=10 (d) y"(!) + 8y'(1) + 16y =0 3. Find the general solution of each differential equation in Prob. 2, and then definitize the solution with the initial conditions y(0) = 4 and y'(0) = 2. 4. Are the intertemporal equilibriums found in Prob. 3 dynamically stable? 5. Verify that the definite solution in Example S indeed (o) satisfies the two initial condi- tions and (b) has first and second derivatives that conform to the given differential equation. 6. Show that, as f - oo, the limit of tell is zero if r