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)

×