Eurler’s equation

Let k be any real number , For a given k and t, x, y > 0 we have the following equation :

F( t*x, t*y ) = t^k * F( x, y )

We can substitute t = 1/x

F ( x, y ) = x^k  * F(1 , y/x )

We can define g(z) = F( 1 , z)

then finally :

F ( x, y )  = x ^ k * g( y/x )

An example could be  : F( x, y ) = x^2 +  4  * y^2  + 3 x*y

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