Program Explanation Given information: The differential equation is d y d x = sin ( x − y ) . Explanation: Consider x − y as v and differentiate with respect to x . x − y = v 1 − d y d x = d v d x d y d x = 1 − d v d x The given differential equation can be written as, 1 − d v d x = sin v d v d x = 1 − sin v 1 1 − sin v d v = d x 1 + sin v ( 1 − sin v ) ( 1 + sin v ) d v = d x Simplify the above equation as, 1 + sin v 1 − sin 2 v d v = d x 1 + sin v cos 2 v d v = d x 1 cos 2 v + sin v cos 2 v = d x sec 2 v + tan v sec v = d x Integrate both sides of above equation

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 1.6, Problem 61P

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Program Description: Purpose of problem is to calculate the solution of the equation dydx=sin(x−y) and check whether the solution contains y(x)=x−π2 as a linear solution.

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Chapter 1.6, Problem 60P

Chapter 1.6, Problem 62P

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Chapter 1 Solutions

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Program Description: Purpose of problem is to calculate the solution of the equation d y d x = sin ( x − y ) and check whether the solution contains y ( x ) = x − π 2 as a linear solution.

Solution Summary: The author explains that the problem is to calculate the solution of the equation dx=mathrmsinleft.

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Program Description: Purpose of problem is to calculate the solution of the equation dydx=sin(x−y) and check whether the solution contains y(x)=x−π2 as a linear solution.

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Chapter 1 Solutions