Does Homogeneity Imply Correctness in Equations?

[Alvl tay]

Homework Statement

Does the fact that a statement is homogeneous mean that it is correct? Explain

Homework Equations

no relevant equations

The Attempt at a Solution

No, it does not mean it is correct. this is because...?

 

[rude man]

First, 'homogeneous' in general parlance does not mean 'correct'. It means 'of uniform consistency'. As in 'homogenized milk' or 'homogeneous societies'.

Second, 'homogeneous' referring to differential equations has very distinct meanings. In fact, there are 2 meanings attached to the term if the d.e. is 1st order, which is nice and confusing, and one for linear d.e.'s of any order.

It's a dumb term. Makes absolutely no sense. But you have to learn to handle d.e.'s in the form described as "homogeneous" anyway.