If u= ⁻¹ ( x^2+y^2 x+y ) then x u x +y u y equal to :

Step-by-step solution

u= ⁻¹ ( x^2+y^2 x+y ) Here u is not a homogeneous function. But f(x, y)= u= x^2+y^2 x+y is a homogeneous function of degree one. Here by Euler's theorem x f x +y f y =f x x ( u)+y y ( u)= u x u u x +y u u y = u x u x +y u y = u