y'(x)=\frac{y(x) \left(y(x) e^{\frac{2 \log ^2(x)}{\log (x)+1}} x^{\frac{2}{\log (x)+1}+2}+y(x) e^{\frac{2 \log ^2(x)}{\log (x)+1}} \log ^2(x) x^{\frac{2}{\log (x)+1}+2}+2 y(x) e^{\frac{2 \log ^2(x)}{\log (x)+1}} \log (x) x^{\frac{2}{\log (x)+1}+2}-e^{\frac{2 \log ^2(x)}{\log (x)+1}} x^{\frac{2}{\log (x)+1}+2}-e^{\frac{2 \log ^2(x)}{\log (x)+1}} \log (x) x^{\frac{2}{\log (x)+1}+2}-1\right)}{x (\log (x)+1)}