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.pngand to differentiate this to a Nonhomogeneous Differential Equation, inspect this:
http://media.wiley.com/Lux/12/257412.image1.pngHope this helps.
Best regards,
Maji
