Program Explanation Given information: The reducible second-order differential equation is, y ″ = 2 y ( y ′ ) 3 Explanation: The given differential equation is, y ″ = 2 y ( y ′ ) 3 Substitute p for y ′ and p d p d y for y ″ in above equation as, p d p d y = 2 y p 3 d p d y = 2 y p 2 d p p 2 = 2 y d y Integrate both sides of above equation. ∫ d p p 2 = 2 ∫ y d y ∫ p − 2 d p = 2 ⋅ y 2 2 + C p − 1 − 1 = y 2 + C 1 p = − y 2 − C Substitute d x d y for 1 p in above equation. d x d y = − y 2 − C d x = − ( y 2 + C ) d y Integrate both sides of above equation

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, 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.

Question

Chapter 1.6, Problem 51P

Program Plan Intro

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

Summary introduction: Problem will use substitution of p=dydx and y″=pdpdy in the second-order differential equation F(y,y′,y″)=0 .

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Chapter 1.6, Problem 50P

Chapter 1.6, Problem 52P

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Chapter 1 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - 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Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y ″ = 2 y ( y ′ ) 3 . Summary introduction: Problem will use substitution of p = d y d x and y ″ = p d p d y in the second-order differential equation F ( y , y ′ , y ″ ) = 0 .

Solution Summary: The author explains that the problem is to calculate the general solution of the differential equation y′′=2y

Concept explainers

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

Summary introduction: Problem will use substitution of p=dydx and y″=pdpdy in the second-order differential equation F(y,y′,y″)=0 .

Want to see the full answer?

Chapter 1 Solutions

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y ″ = 2 y ( y ′ ) 3 . Summary introduction: Problem will use substitution of p = d y d x and y ″ = p d p d y in the second-order differential equation F ( y , y ′ , y ″ ) = 0 .

Solution Summary: The author explains that the problem is to calculate the general solution of the differential equation y′′=2y

Concept explainers

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y″=2y(y′)3 . Summary introduction: Problem will use substitution of p=dydx and y″=pdpdy in the second-order differential equation F(y,y′,y″)=0 .

Want to see the full answer?

Chapter 1 Solutions

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

Summary introduction: Problem will use substitution of p=dydx and y″=pdpdy in the second-order differential equation F(y,y′,y″)=0 .