Question #223859

Eliminate the arbitrary function from 2=xy+f(x^2+y^2) to obtain the partial differencial equation.

Expert's answer

From means that the solution of the partial differential equation is given by an arbitrary function of class C_{2} 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 :

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