Program Explanation Given information: The first-order differential equation is x e y y ′ = 2 ( e y + x 3 e 2 x ) . Explanation: Consider e y as t and differentiate with respect to x . e y d y d x = d t d x The given differential equation can be written as, x d t d x = 2 ( t + x 3 e 2 x ) = 2 t + 2 x 3 e 2 x d t d x = 2 t x + 2 x 3 e 2 x x d t d x − 2 x t = 2 x 2 e 2 x The above equation is a linear first-order equation and its solution can be calculated as, t e − 2 ∫ 1 x d x = 2 ∫ x 2 e 2 x e − 2 ∫ 1 x d x d x t e − 2 ln x = 2 ∫ x 2 e 2 x e − 2 ln x d x t e ln x − 2 = 2

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 28P

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation xeyy′=2(ey+x3e2x) .

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Chapter 1.6, Problem 27P

Chapter 1.6, Problem 29P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation x e y y ′ = 2 ( e y + x 3 e 2 x ) .

Solution Summary: The author explains that the first-order differential equation is xeyprime =2left.

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation xeyy′=2(ey+x3e2x) .

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Chapter 1 Solutions