Computer: Phase-Plane Trajectories: Each of the functions in Problems 1-3 is the solution of a linear second-order differential equation with constant coefficients. In each case, do the following:
(a) Determine the DE.
(b) Calculate the derivative y' and the initial condition y(0), y'(0).
(c) Plot the trajectory [y(t), y'(t)] on the vector field in the yy' -plane.
1. y(t) = 2e-t + e-31
2. y(t) = e-t + e-81
3. y(t) = et + e-1