Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 68

Given,
f(x,y) =x^3 + 3x^2y^2-2y^2
to check whether it is homogenous or not
f(tx,ty)=(tx)^3 +3(tx)^2 (ty)^2 - 2(ty)^2
=t^3 x^3+3 t^4 x^2y^2 -2t^2y^2
=t^2(t x^3 +3t^2 x^2y^2 -2y^2)
so this is not of the form
f(tx,ty)=t^n f(x,y)
and so the function f(x,y) is not homogenous