onsider the system dx dt = y dy dt = x (a) Which of the following is the general solution of the system?(1) i. x(t) = C1 cos t + C2 sin t, y(t) = C2 cos t C1 sin t. ii. x(t) = C1et + C2et, y(t) = C1et + C2et. iii. x(t) = C1et cos t + C2et sin t, y(t) = C1(et sin t et cos t) + C2(et cos t et sin t). For the rest of the problem, we'll focus on a particular solution. (b) Find the solution satisfying the initial conditions x(0) = 2 and y(0) = 2. (c) Say what happens in the long term to this particular solution that is, what are lim t x(t) and lim t y(t)? (d) Pick the picture (of the following three) that shows the solution trajectory in the phase plane: (1)You are not expected to be able to actually solve the systems, but you should be able to check whether something is a solution to a given system. 1