Hello, I have a mid term tomorrow and this question was on the practice mid term and our prof has not posted any solutions. I tried to catch him after class but there was a million other students crowding him. If there is anyone who could give me a hand with this I would appreciate it.
Show that if f is any homogeneous function of degree n, then it
satises Euler's formula
xD1f(x; y) + yD2f(x; y) = nf(x; y):
Hint: Treat each side of the dening equation as a function of 3
variables t; x and y, and use the chain rule to compute the partials
with respect to t. Then set t = 1.