
Concept explainers
A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular
- (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 y-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 y 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. [Hint: Let z = dy/dx in the differential equation and solve the resulting first-order equation to find z; then integrate z to find y.]
- (c) Does the dog ever catch the rabbit

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Chapter 9 Solutions
Single Variable Calculus
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