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# Prove that if a trajectory starts at a noncritical point of the system dx dt = F( x, y) ISBN: 9781119256007 392

## Solution for problem 23 Chapter 9.2

Elementary Differential Equations and Boundary Value Problems | 11th Edition

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Problem 23

Prove that if a trajectory starts at a noncritical point of the system dx dt = F( x, y), dy dt = G( x, y), then it cannot reach a critical point ( x0, y0) in a finite length of time. Hint: Assume the contrary; that is, assume that the solution x = (t), y = (t) satisfies (a) = x0, (a) = y0. Then use the fact that x = x0, y = y0 is a solution of the given system satisfying the initial condition x = x0, y = y0 at t = a. 2

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##### ISBN: 9781119256007

This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 11. The answer to “Prove that if a trajectory starts at a noncritical point of the system dx dt = F( x, y), dy dt = G( x, y), then it cannot reach a critical point ( x0, y0) in a finite length of time. Hint: Assume the contrary; that is, assume that the solution x = (t), y = (t) satisfies (a) = x0, (a) = y0. Then use the fact that x = x0, y = y0 is a solution of the given system satisfying the initial condition x = x0, y = y0 at t = a. 2” is broken down into a number of easy to follow steps, and 97 words. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9781119256007. The full step-by-step solution to problem: 23 from chapter: 9.2 was answered by , our top Math solution expert on 03/13/18, 08:17PM. Since the solution to 23 from 9.2 chapter was answered, more than 210 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 75 chapters, and 1655 solutions.

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