Why are these DEs homogeneous?

[bcjochim07]

Homework Statement

The following DEs are homogeneous and can be solved using a substitution y=ux or v=xy. I can solve them, I'm just don't see how they are homogeneous.

How is it that with there being an exponent (y/x) that this is homogeneous. I don't see how I could pull out t^$$\alpha$$

(x + ye^(y/x))dx - (xe^(y/x))dy = 0

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Same problem with this one

ydx + x(lnx - lny -1)dy=0

For both, I can see the powers are the same, but I don't think I completely understand what it means to have a homogeneous differential equation.

Homework Equations

The Attempt at a Solution

 

[bcjochim07]

also this one is bothering me x(dy/dx) = y ln(xy)