Program Explanation Given information: The differential equation is d y d x = 2 y − x + 7 4 x − 3 y − 18 . Explanation: The solution of the differential equation d u d v = u − v u + v is v 2 + 2 u v − u 2 = C . The intersection point of the lines 2 y − x + 7 = 0 and 4 x − 3 y − 18 = 0 are calculated as, 4 ( 2 y − x + 7 ) + 4 x − 3 y − 18 = 0 8 y − 3 y = − 10 5 y = − 10 y = − 2 The value of x is calculated as, − x − 4 + 7 = 0 x = 7 − 4 = 3 The intersection point of the lines 2 y − x + 7 = 0 and 4 x − 3 y − 18 = 0 are ( 3 , − 2 ) , so the value of h is 3 and the value of k is − 2 . The value of u in terms of x is calculated as, x = u + h x − 3 = u u = x − 3 The value of v in terms of y is calculated as, y = v + k v = y − ( − 2 ) = y + 2 The given differential equation can be written as, d v d u = 2 ( v − 2 ) − ( u + 3 ) + 7 4 ( u + 3 ) − 3 ( v − 2 ) − 18 = 2 v − u 4 u − 3 v = u ( 2 v u − 1 ) u ( 4 − 3 v u ) = 2 ⋅ v u − 1 4 − 3 ⋅ v u Consider z = v u and differentiate. d d u ( u z ) = d v d u z + u d z d u = d v d u Now, the given homogeneous equation can be written as, z + u d z d u = 2 z − 1 4 − 3 z u d z d u = 2 z − 1 4 − 3 z − z = 2 z − 1 − z ( 4 − 3 z ) 4 − 3 z = 3 z 2 − 2 z − 1 4 − 3 z Simplify the above equation. 3 z − 4 3 z 2 + − 2 z − 1 d z = − d u u Integrate both sides of above equation. ∫ 3 z − 4 3 z 2 − 2 z − 1 d z = − ∫ d u u ......

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 60P

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Program Description: Purpose of problem is to calculate the solution of the differential equation dydx=2y−x+74x−3y−18 .

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Chapter 1.6, Problem 59P

Chapter 1.6, Problem 61P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose of problem is to calculate the solution of the differential equation d y d x = 2 y − x + 7 4 x − 3 y − 18 .

Solution Summary: The author explains the purpose of the problem, which is to calculate the solution of a differential equation.

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Program Description: Purpose of problem is to calculate the solution of the differential equation dydx=2y−x+74x−3y−18 .

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Chapter 1 Solutions