Using Euler's theorem of homogeneous functions

[Prometheus]

Been stuck on this question:

 

show g is homogeneous of degree k and state the value of k.

 

[latex]g(x, y)= x^3 +3xy^2/ \sqrt[3]{x^2-y^2}[/latex]

 

So i've been trying to use:

 

[latex]kg(x,y)=x\dfrac{\delta g}{\delta x}+y\dfrac{\delta g}{\delta y}[/latex]

 

but i just can't seem to get a solution for k. Am i going about this the right way? I think i'm missing something obvious. Does anyone know of anywhere with worked examples of these types of questions?

 

Thanks for any help.