Question

if u=cos^-1(x/y)+tan^-1(y/x) then find x^2uxx+2xyuxy+y^2uyy
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Answer 1

Answer:

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Step-by-step explanation:

u = sin-1 (x/y) + tan-1(y/x)

= sin-1 (1/(y/x)) + tan-1(y/x)

= x0f(y/x)

Here u is a homogeneous function of degree 0.

Here n = 0

So by Euler’s theorem

x∂u/∂x + y ∂u/∂y = nu

x∂u/∂x + y ∂u/∂y = 0

Hence option (1) is the answer.