Re: " Are there known ways to solve g(3*x/(x+1), y) = d/dy g(x,y) - 2/y*g(x,y) ? "

In article <1139060020.151801.178190@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<alainverghote@xxxxxxxx> wrote:

Dear Friends ,

I am looking for ways to solve the given
functional equation g:R^2 -> R continuously
differentiable for x and y .

We may consider the following process:
when x => 3*x/(x+1) , g => (d/dy - 2/y ) o g

Wait for your help ,

Alain.


I would say: change variables appropriately, then you have to solve

C(x+1,y) = (d/dy) C(x,y)

For this, define C(x,y) any way you like for 0 <= x < 1, then
the other values are multiple derivatives (or integrals) of this.
[Of course, for each x, the function C(x,y) should have infinitely
many integrals and derivatives.]
.