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**Liverpool** __Problem__:

If F is homogeneous of degree k in x and y, F can be written in the form:

$\displaystyle F=x^k g\left(\frac{y}{x}\right)$

Use that to prove the following equation for F:

$\displaystyle xF_x+yF_y=kF$

__Solution__:

I found that:

$\displaystyle xF_x=kx^kg\left(\frac{y}{x}\right)-x^{k-1}y g_x\left(\frac{y}{x}\right)$

and

$\displaystyle yF_y=x^{k-1} y g_y\left(\frac{y}{x}\right) $

Adding them:

$\displaystyle xF_x+yF_y=kx^k g\left(\frac{y}{x}\right)-x^{k-1}y g_x\left(\frac{y}{x}\right)+x^{k-1} y g_y\left(\frac{y}{x}\right)$

Now, I stopped!

any help?