Thread: level curves implying a separate differentiable function

Suppose f:R^2 - {0} → R is a differentiable function whose gradient is nowhere 0 and that satisfies -y(df/dx) + x(df/dy) = 0 everywhere

the level curves of f are of the form (x,-y)

Show that there s a differentiable function F defined on the set of positive real numbers such that f(x) = F(||x||)