Program Explanation Given information: The first-order differential equation is x 2 y ′ + 2 x y = 5 y 4 . Explanation: The given differential equation can be rewritten as, d y d x + 2 x y x 2 = 5 y 4 x 2 d y d x + 2 x y = 5 x 2 y 4 Compare the Bernoulli equation with the above equation to obtain the value of P ( x ) and Q ( x ) . P ( x ) = 2 x Q ( x ) = 5 x 2 The value of n is 4 and the value of 1 − n is calculated as, 1 − n = 1 − 4 = − 3 Substitute y − 3 for v and differentiate with respect to x as, v = y − 3 y = v − 1 3 d y d x = − 1 3 v − 4 3 d v d x The given differential equation can be written as, − 1 3 v − 4 3 d v d x + 2 x v − 1 3 = 5 x 2 ( v − 1 3 ) 4 − 1 3 v − 4 3 d v d x + 2 x v − 1 3 = 5 x 2 v − 4 3 − 1 3 v − 4 3 ( d v d x − 6 x v ) = 5 x 2 v − 4 3 d v d x − 6 <

5th Edition

ISBN: 9780135904206

Author: Edwards

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 22P

Program Plan Intro

Program Description: Purpose of problem is to calculate the general solution of the differential equation x2y′+2xy=5y4 .

Summary introduction: Problem will use 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 21P

Chapter 1.6, Problem 23P

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Chapter 1 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x 2 y ′ + 2 x y = 5 y 4 . Summary introduction: Problem will use 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 the purpose of the problem, which is to calculate the general solution to the first-order differential equation x2yprime

Concept explainers

Program Description: Purpose of problem is to calculate the general solution of the differential equation x2y′+2xy=5y4 .

Summary introduction: Problem will use 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 Solutions

Program Description: Purpose of problem is to calculate the general solution of the differential equation x 2 y ′ + 2 x y = 5 y 4 . Summary introduction: Problem will use 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 the purpose of the problem, which is to calculate the general solution to the first-order differential equation x2yprime

Concept explainers

Program Description: Purpose of problem is to calculate the general solution of the differential equation x2y′+2xy=5y4 . Summary introduction: Problem will use 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 of problem is to calculate the general solution of the differential equation x2y′+2xy=5y4 .

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