Name: ID: MATH 304 DIFFERENTIAL EQUATIOS Section: Date: 1. Solve the following initial value problem and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. dy 2y-10, y(0) = Yo dt 2. Consider the falling object of mass 10 kg in Example 2 but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as dv 1 dt (492 v) 245 Also see Problem 21 of Section 1.1. b. If v(0) = 0, find an expression for v(t) at any time. c. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part c, compare the effect of a quadratic drag force with that of a linear drag force. e. Find the distance x(t) that the object falls in time t . f. Find the time T it takes the object to fall 300 m.