9. För each of the following equations, decide the solution given is asymptotically stable, stable but not asymptotically stable, or unstable. (a) y" = 0, 4(t) = 0. (c) y"+ 4y = 0, $(t) = 0. (e) y" + 4y' +4y =0, 6(t) = 0. (g) y" – 4y = 0, $(t) = 0. (b) y" = 0, 6(t) =t. (d) y" + 4y = 0, $(t) = cos 2t. (f) y" + 4y' + 4y 0, 6(t) = e-2". (h) y" – 4y = 0, $(t) = e-2". %3D

Use the convolution to write a formula for problem: y" – 3y' + 2y = f(t), y(0) = 1, y'(0) = 0;

2- A hot-air balloon is moving vertically up and down so that its height relative to the ground is given by h(t)=t³ – t? -t +1, where "h" is measured in kilometers and t In hours. If the height h was recorded between the first and the second hour of motion 0s ts2 find. a- The velocity of the hot-air balloon at t=1h. b- The acceleration of the balloon when the velocity is zero.

2. Assume that the population of a colony of Brazilian fire ants, P, is described by the function P(t)= \t+1·e-0.5t is measured in days (t=0 when one begins monitoring the population). (a) Find the initial population, P(0) (include units with your answer). +10t +200. The population here is measured in thousands of individuals, and time, t, %3D %3D (b) Find P (t). (c) Evaluate P (0) (include units with your answer).