According to Euler theorem, x du/dx + y du/**dy = nu; where n is degree of the homogeneous equation.**
Now,
u = ax2+ 2hxy + by**2
du/dx = 2ax + 2hy
du/dy = 2hx + 2by
L.H.* = x du/dx + y du/dy
x(2ax + 2hy) + y(2hx + 2by)
= 2ax2 + 2hxy + 2hxy + 2by2
= 2(*ax*2+ 2hxy + by2) = 2u
Thus Euler theorem verified.
