Show transcribed image text 145 ations 1-10, write an equivalent first-order system in the form given ss .mine the dimension of the system and state whether or not it is linear, and if lincar, whether or not it is homogeneous. 1, x" + 5x' + 2x = sin(1) 2.x” + 21x, + x = 0 3.x", + 4x" + 3x = 2+1 5, x' = y, y' =-x 6, x" = x + y, y' = 5x 7, x' = xy, y'" = x + y', + y2 8.x', = x + z,y, =xy, z' = y + x + 2z Hint: First solve the two equations for x' and y 10.x', + y, + 2x-3y = 0, y' + 2y = x', 11. Two predators X and Y, living on a single prey Z, are interacting in a closed ecosys- tem. Letting x(). y(G), and z(t) be the size (in hundreds of individuals) of the three populations at time t, the equations of growth are given as (4.5) z'(1) = qz (1)(1-z (1))-2(1)(kx(t) + my(1)), where the parameters r,s.q. a,b,c, k, and m are all assumed to be positive. (a) Is this system linear? Explain. (b) How does the predator X affect the growth of the prey population? (e) If the prey dies out, what will happen to the predator X over the long run? Explain. (d) If the predators both disappear, what will happen to the prey population over the long run? Explain. ith three sorings A, B, and C and two objects