Program Explanation Given information: The differential equation is d y d x + 2 x y = 1 + x 2 + y 2 . One particular solution of Riccati equation is y 1 ( x ) = x . Explanation: The Riccati equation is, d y d x = A ( x ) y 2 + B ( x ) y + C ( x ) The given differential equation can be written as, d y d x = 1 + x 2 + y 2 − 2 x y = 1 + ( x − y 2 ) Consider x + 1 v as y and differentiate with respect to x . 1 − 1 v 2 d v d x = d y d x Substitute 1 − 1 v 2 d v d x for d y d x in given differential equation. 1 − 1 v 2 d v d x = 1 + ( x − y ) 2 − 1 v 2 d v d x = ( x − y ) 2 The value of x − y is calculated as, y = x + 1 v x − y = − 1 v Now, the given differential equation can be written as, −

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 1.6, Problem 65P

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Program Description: Purpose ofproblem is to calculate solution of the differential equation dydx+2xy=1+x2+y2 .

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Chapter 1.6, Problem 64P

Chapter 1.6, Problem 66P

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Find A PARTICULAR solution of the following differential equation by using UNDE-TERMINED COEFFICIENTS METHOD. y” + 3y’ + 2y = ex sin x

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose ofproblem is to calculate solution of the differential equation d y d x + 2 x y = 1 + x 2 + y 2 .

Solution Summary: The author explains that the Riccati equation is y_1(x)=x.

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Program Description: Purpose ofproblem is to calculate solution of the differential equation dydx+2xy=1+x2+y2 .

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Chapter 1 Solutions