Program Explanation Given information: The reducible second-order differential equation is, y ′ = y + y 3 Explanation: The given differential equation can be rewritten as, d y d x − y = y 3 Compare the Bernoulli equation with the above equation to obtain the value of P ( x ) and Q ( x ) . P ( x ) = − 1 Q ( x ) = 1 The value of n is 3 and the value of 1 − n is calculated as, 1 − n = 1 − 3 = − 2 Substitute y − 2 for v and differentiate with respect to x as, v = y − 2 y = v − 1 2 d y d x = − 1 2 v − 3 2 d v d x The given differential equation can be written as, − 1 2 v − 3 2 d v d x − v − 1 2 = ( v − 1 2 ) 3 − 1 2 v − 3 2 ( d v d x + 2 v ) = v

5th Edition

ISBN: 9780100802452

Author: Calvis

Publisher: YUZU

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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 21P

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y′=y+y3 .

Summary introduction: Problem will use the Bernoulli equation of the form dydx+P(x)y=Q(x)yn and then the substitution v=y1−n .

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Chapter 1.6, Problem 20P

Chapter 1.6, Problem 22P

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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 ′ = y + y 3 . Summary introduction: Problem will use the Bernoulli equation of the form d y d x + P ( x ) y = Q ( x ) y n and then the substitution v = y 1 − n .

Solution Summary: The author explains that the problem uses the Bernoulli equation of the form ydx+P(x.

Concept explainers

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y′=y+y3 .

Summary introduction: Problem will use the Bernoulli equation of the form dydx+P(x)y=Q(x)yn and then the substitution v=y1−n .

Want to see the full answer?

Chapter 1 Solutions

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y ′ = y + y 3 . Summary introduction: Problem will use the Bernoulli equation of the form d y d x + P ( x ) y = Q ( x ) y n and then the substitution v = y 1 − n .

Solution Summary: The author explains that the problem uses the Bernoulli equation of the form ydx+P(x.

Concept explainers

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y′=y+y3 . Summary introduction: Problem will use the Bernoulli equation of the form dydx+P(x)y=Q(x)yn and then the substitution v=y1−n .

Want to see the full answer?

Chapter 1 Solutions

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation y′=y+y3 .

Summary introduction: Problem will use the Bernoulli equation of the form dydx+P(x)y=Q(x)yn and then the substitution v=y1−n .