Show that dy/dx=(x^2+xy+y^2)/x^2 is homogeneous.

WYZANT.COM
CREATE FREE ACCOUNT
Sign In

Access thousands of free resources from expert tutors

Comment on posts and interact with the authors

Ask questions and get free answers from tutors

View videos, take interactive quizzes, and more!

Show that dy/dx=(x^2+xy+y^2)/x^2 is homogeneous.

Tutors, please sign in to answer this question.

x^2 dy - (x^2+xy+y^2) dx = 0

x^2 and x^2+xy+y^2 are homogeneous functions of the same degree 2.

Therefore, dy/dx=(x^2+xy+y^2)/x^2 is homogeneous.

--------------

Definition of homoegeneous diffeential equations:

A homogeneous differential equation is an equation of the form M(x, y)dx + N(x, y)dy = 0

where M and N are homogeneous functions of hte same degree.

- Algebra 904
- Algebra 1 632
- Math Help 595
- Algebra 2 488
- Trigonometry 164
- Geometry 262
- Prealgebra 37
- Science 36
- Word Problem 401
- Precalculus 102