Question

If u = ax² +2hxy+${by}^{2}$

then prove that
x du/dx +y du/dy = 2u​

Answer 1

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Answer 2

Answer:

GIVES THAT –

$u = a {x}^{2} + 2hxy + b {y}^{2}$

TO PROVE :-

$x \frac{du}{dx} + y \frac{du}{dy} = 2u$

=》

$\frac{du}{dx} = 2ax + 2hy$

AND –

$\frac{du}{dy} = 2hx + 2by$

L.H.S. =

$x \frac{du}{dx} + y \frac{du}{dy} = 2a {x}^{2} + 2hxy + 2hxy + 2b {y}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(a {x}^{2} + 2hxy + b {y}^{2} )\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2u$

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