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

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.

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

EBK DIFFERENTIAL EQUATIONS

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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 .