Teacher did not go over vectors at all in class so i have no idea how to any these
Problem 5: Using vector fields to understand solutions to DEs. Problem 5: Using vector fields to u (a) Sketch the vector field corresponding to the second order differential equation y" -4y in the y-y-plane. Based on this information, (i) roughly sketch the graph of a solution y(t) in the y-t plane if y(0) = 1 and y'(0) = 0 and finally (ii) try to guess an explicit solution to the equation y"--4y satisfying y(0) = 5. (a) Sketch the vector field corresponding to the second order differential equation y- 2y yin the y-y'-plane. Based on this information, (i) roughly sketch the graplh of a solution y(t) in the y-t plane if y(0) =-3 and y(0) = 2 and finally (ii) try to guess an explicit solution to the equation y"-2y + y, satisfying y(0) = y(1) = 1.
