Set 29 - Second-Order Differential Equations II 1. (a) Find the solution of x 10x 9x = 0 satisfying the initial conditions x(0) = 8 and x(0) = 0. (b) Find the solution of x 6x 9x = 0 satisfying the initial conditions x(0) = 8 and x(0) = 0. (c) Hinged doors often have "door closers" which automatically swing the doors shut after they have been opened. Often, the door closer contains a spring that is at equilibrium when the door is shut. The door closer can be adjusted (which essentially adjusts the amount of friction); in most cases, the goal is to adjust the door closer so that the door closes quickly but smoothly. Use a calculator or computer to graph the solutions you found in (a) and (b) together. Which one returns to 0 more quickly?(1) Is this the one with more or less friction? (Does this make sense to you intuitively?) (d) (Exploratory) What happens if you continue to adjust the friction in the "better" direction? (That is, if you thought more friction made the spring return to 0 more quickly, what happens if you increase the friction even more? If you thought less friction