A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular coordinate system (as shown in the figure), assume:
(i) The rabbit is at the origin and the dog is at the point (L, 0) at the instant the dog first sees the rabbit.
(ii) The rabbit runs up the -axis and the dog always runs straight for the rabbit.
(iii) The dog runs at the same speed as the rabbit.
(a) Show that the dog€™s path is the graph of the function y = f(x), where satisfies the differential equation

(b) Determine the solution of the equation in part (a) that satisfies the initial conditions y = y€™ = 0 when x = L.
(c) Does the dog ever catch the rabbit?

d'y dx 2 dy dx