Program Explanation Given information: The differential equation is x ( x + y ) y ′ + y ( 3 x + y ) = 0 . Calculation: The given differential equation can be written as, x ( x + y ) d y d x = − y ( 3 x + y ) d y d x = − y ( 3 x + y ) x ( x + y ) = − y x ⋅ x ( 3 + y x ) x ( 1 + y x ) = − y x ( 3 + y x 1 + y x ) Substitute v = y x and differentiate with respect to x . x v = y d d x ( x v ) = d y d x v d x d x + x d v d x = d y d x v + x d v d x = d y d x Now, the given differential equation can be written as, v + x d v d x = − v ( 3 + v 1 + v ) x d v d x = − v ( 3 + v 1 + v ) − v = − v ( 3 + v ) − v ( 1 + v ) 1 + v = − 3 v − v 2 − v − v 2 1 + v Simplify the above equation. x d v d x = − 4 v − 2 v 2 1 + v = − 2 v ( 2 + v ) 1 + v 1 + v − 2 v ( 2 + v ) d v = d x x − 1 2 ( 1 + v v ( 2 + v ) ) d v = d x x Apply partial fraction decomposition to simplify the expression 1 + v v ( 2 + v ) as, 1 + v v ( 2 + v ) = A v + B 2 + v = A ( 2 + v ) + B v v ( 2 + v )

5th Edition

ISBN: 8220100802454

Author: Calvis

Publisher: PEARSON

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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 15P

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x(x+y)y′+y(3x+y)=0 .

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Chapter 1.6, Problem 14P

Chapter 1.6, Problem 16P

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Write a c++ program that will count from 1 to 10 by 1. The default output should be: 1, 2, 3, 4, 5, 6 , 7, 8, 9, 10 There should be only a newline after the last number. Each number except the last should be followed by a comma and a space. To make your program more functional, you should parse command line arguments and change behavior based on their values. Argument Parameter Action -f, --first yes, an integer Change place you start counting -l, --last yes, an integer Change place you end counting -s, --skip optional, an integer, 1 if not specified Change the amount you add to the counter each iteration -h, —help none Print a help message including these instructions. -j, --joke none Tell a number based joke. So, if your program is called counter, counter -f 10 --last 4 --skip 2 should produce 10, 8, 6, 4 Please use the last supplied argument. If your code is called counter, counter -f 4 -f 5 -f 6 should count from 6. You should…

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x ( x + y ) y ′ + y ( 3 x + y ) = 0 .

Solution Summary: The author explains that the problem is to calculate the general solution of the differential equation x(x+y).

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x(x+y)y′+y(3x+y)=0 .

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Chapter 1 Solutions