What is a Homogeneous Differential Equation and How Can I Identify One?

can anybody explain what is Homogenous Differential Equation

Hi

Here is a video tutorial from khanacademy that I believe will help you understand Homogenous Equations: https://www.khanacademy.org/math/differential...-equations/v/first-order-homegenous-equations

Check it out, Hope it helps.

Kevin

Hi Trish,

If we will just simplify explanation of a Homogeneous Differential Equation in a first-order ordinary differential equation, in the form of:

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

_
If both functions M(x,y) and N(x,y) are homogeneous functions of the same degree.

To test, we multiply each variable by a parameter lambda, lambda

we find:
M(lambda x, lambda y) = lambda^n M(x,y)
and
N(lambda x, lambda y) = lambda^n N(x,y)

Some books gives you visual inspection, this is done by checking that your ordinary differential equation involves only derivatives of y and terms involving y and they're set to 0, like this:
http://media.wiley.com/Lux/11/257411.image0.png

and to differentiate this to a Nonhomogeneous Differential Equation, inspect this:
http://media.wiley.com/Lux/12/257412.image1.png

Hope this helps.

Best regards,

Maji

Hi,
Here is a link
http://tutorial.math.lamar.edu/Classes/DE/DE.aspx
this worked for me earlier may be helpful to you.