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N 24. Consider the equation or by s. Try E each dy y-4x x-yiousupo lsinonsi (29) dx a. Show that equation (29) can be rewritten as dy v/x) - 4 1- (y/x)* (30) dx thus equation (29) is homogeneous. b. Introduce a new dependent variable v so that v = y = xv(x). Express dy/dx in terms of x, v, and dv/dx. c. Replace y and dy/dx in equation (30) by the expressions from part b that involve v and dv/dx. Show that the resulting differential equation is re the = y/x, or noilagitesv (8Yand 1-y dalsto re the dv v+x- ソ-4 dx I The word 小一本

N 24. Consider the equation or by s. Try E each dy y-4x x-yiousupo lsinonsi (29) dx a. Show that equation (29) can be rewritten as dy v/x) - 4 1- (y/x)* (30) dx thus equation (29) is homogeneous. b. Introduce a new dependent variable v so that v = y = xv(x). Express dy/dx in terms of x, v, and dv/dx. c. Replace y and dy/dx in equation (30) by the expressions from part b that involve v and dv/dx. Show that the resulting differential equation is re the = y/x, or noilagitesv (8Yand 1-y dalsto re the dv v+x- ソ-4 dx I The word 小一本

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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on yx only, of using them to invest sciences. One reason fo Homogeneous relating the variables make predictions abou often easy to vary para. then the equation is said to be homogeneous.' Such equations dependent variable. Problem 24 illustrates how to solve first-order always be transformed into separable equations by a change of the can a change of the %3D dy/dx = f(x, y) can be expressed as always be transformed into separable equations by very time-consuming mathematical modelin homogeneous equations. N 24. Consider the equation ugh 22 can be lytically or by solutions. Try somewhat complemer by comparison of thei analyses may suggest indicate fairly precise In Sections 1.1 a dyy-4x x-yiousupo Isinoo (29) dx antages of each We begin by recapi sections. Regardless are always present i a. Show that equation (29) can be rewritten as dy (y/x) – 4 dx 1- (y/x) qmoo vd (30) id. ints where the Step 1: Construc thus equation (29) is homogeneous. b. Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. c. Replace y and dy/dx in equation (30) by the expressions from part b that involve v and dy/dx. Show that the resulting differential equation is into mathematical critical at this stage process. For exam warmer to a cooler about in accordand adi nerli noilsgi129 (8Yond dx ¯ T - v' ol Esto d. ints where the at a rate proportic dv v+x- ソー4 こ I The word "homogeneous" has different contexts. The homogeneois the homogene I value. II
Transcribed Image Text:on yx only, of using them to invest sciences. One reason fo Homogeneous relating the variables make predictions abou often easy to vary para. then the equation is said to be homogeneous.' Such equations dependent variable. Problem 24 illustrates how to solve first-order always be transformed into separable equations by a change of the can a change of the %3D dy/dx = f(x, y) can be expressed as always be transformed into separable equations by very time-consuming mathematical modelin homogeneous equations. N 24. Consider the equation ugh 22 can be lytically or by solutions. Try somewhat complemer by comparison of thei analyses may suggest indicate fairly precise In Sections 1.1 a dyy-4x x-yiousupo Isinoo (29) dx antages of each We begin by recapi sections. Regardless are always present i a. Show that equation (29) can be rewritten as dy (y/x) – 4 dx 1- (y/x) qmoo vd (30) id. ints where the Step 1: Construc thus equation (29) is homogeneous. b. Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. c. Replace y and dy/dx in equation (30) by the expressions from part b that involve v and dy/dx. Show that the resulting differential equation is into mathematical critical at this stage process. For exam warmer to a cooler about in accordand adi nerli noilsgi129 (8Yond dx ¯ T - v' ol Esto d. ints where the at a rate proportic dv v+x- ソー4 こ I The word "homogeneous" has different contexts. The homogeneois the homogene I value. II
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