Question

Does the function f(x,y)= (x^2-y^2)/(x^2+y^2), x

Answer 1

Given function,

$f(x)=\dfrac{x^2-y^2}{x^2+y^2}$

let $y=vx~~~~-(1)$

$\dfrac{dy}{dx}=\dfrac{x^2-v^2x^2}{x^2+v^2x^2}$

$=\dfrac{1-v^2}{1+v^2}$

Hence The degree of numerator and denominator is same, So Given function is Homogeneous.