= 4x2 + 7xy +

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
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Homogeneous DE

M(x,y)dx + N(x,y)dy = 0

is Homogeneous if both M and N are homogeneous functions of the same order.

A function f(x,y) is called homogeneous of degree n if

f(ʎx, ʎy) = ʎnf(x,y)

 

Solution Steps:

Objective: To reduce into a Variable Separable Form

a. Replace y by ux or x by vy

if y = ux, dy = udx + xdu . Use y=ux if N is simpler in form.

if x = vy, dx = vdy + ydv . Use x=y if M is simpler in form

b. Simplify the resulting equation

c. Separate the variables

d. Integrate both sides of the equation to get the General Solution

e. Substitute u = y/x or v =  x/y to have the GS in terms of x and y

have C which is arbitrary constant

 

Solve the DE. (Homogeneous DE)

1. x2y' = 4x2 + 7xy + 2y2

 

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