For the function,

$\displaystyle u(x,y) = x^{2}f(\frac{y}{x})$

determine whether the following statement is true or false,

$\displaystyle x\frac{\partial{u}}{\partial{x}} + y\frac{\partial{u}}{\partial{y}} = 2u$

Now I realize this can be quickly checked by the use of the chain rule, but isn't there an easier way to verify this since one can see that the statement we are being asked to check is in facta positively homogenous function of degree 2?

It's almost identical to the statement forEuler's Theoremin my textbook, but I don't fully understand how this will help our current situation.

Would someone care to explain?