Determining a homogenous differential equation. Why is it that $$f(x,y)=\frac {\cos x^2}{x+y}$$ is not considered homogeneous?

Because in general we do not have
$$\cos\left(\frac{(tx)^2}{tx+ty}\right)=t^k\cos\left(\frac{x^2}{x+y}\right).$$
Edit: The function has been reinterpreted  by an editor. The basic reason remains the same, details are slightly different.
