wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

What is the meaning of a homogeneous equation?


Open in App
Solution

Homogeneous Equation:

A differential equation of the form dydx=fx,y is said to be homogeneous if fx,y is a homogeneous function of degree 0.

Whereas the function fx,y is to be homogeneous function of degree n if for any non-zero constant λ, fλx,λy=λnfx,y

For example: dydx=x2-4y23xy-5x2is a homogeneous differential equation.

We have fx,y=x2-4y23xy-5x2

For any non-zero constant λ, we have

fλx,λy=λx2-4λy23λxλy-5λx2fλx,λy=λ2x2-4y2λ23xy-5x2fλx,λy=λ0x2-4y23xy-5x2fλx,λy=λ0fx,y

So, fx,y is a homogeneous function of degree 0.

Thus, dydx=x2-4y23xy-5x2is a homogeneous differential equation.


flag
Suggest Corrections
thumbs-up
17
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Methods of Solving First Order, First Degree Differential Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon