verify eullors theorm for z=ax²+2hxy+by²
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Step-by-step explanation:
According to Euler theorem, x du/dx + y du/dy = nu; where n is degree of the homogeneous equation.
Now, u = ax2 + 2hxy + by2
du/dx= 2ax + 2hy
du/dy = 2hx + 2by
L.H.S = x du/dx + y du/dy
x(2ax + 2hy) + y(2hx + 2by)
= 2ax2 + 2hxy + 2hxy + 2by2
= 2(ax2 + 2hxy + by2) = 2u
Thus Euler theorem verified
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