A calculus problem by Jeremy marquardt

Calculus Level pending

\(f(x)\) is the solution to the differential equation \(2x = \dfrac{y^{\ln(x)}}{1+(x^{\ln(y)})^2}\ln(x^{\frac{y'}{y}}y^{\frac{1}{x}})\) what is \(\displaystyle \lim_{x\rightarrow 0} \ln(f(\sqrt[2]{\arctan(x)}))\) (assume the constant of integration is zero)

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