Eliminate the arbitrary function from 2=xy+f(x^2+y^2) to obtain the partial differencial equation.
From means that the solution of the partial differential equation is given by an arbitrary function of class C2 with respect to variables x , y. Take , so obtain .
Differentiating respect to x and y and taking gives
.Eliminating and from the above equation gives .
Assuming x + y #0 leads to .Follows the required partial differential equation :