verify Euler's theorem for Z=ax2+by2
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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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