2.629   ODE No. 629

\[ y'(x)=\frac {(2 y(x) \log (x)-1)^2}{x} \] Mathematica : cpu = 0.855755 (sec), leaf count = 47


\[\left \{\left \{y(x)\to \frac {1}{\sqrt {2} \left (\sqrt {2} \log (x)-\tan \left (\frac {1}{2} \left (2 \sqrt {2} \log (x)+\sqrt {2} c_1\right )\right )\right )}\right \}\right \}\] Maple : cpu = 0.225 (sec), leaf count = 62


\[y \relax (x ) = \frac {\sin \left (\ln \relax (x ) \sqrt {2}\right ) c_{1}-\cos \left (\ln \relax (x ) \sqrt {2}\right )}{\sin \left (\ln \relax (x ) \sqrt {2}\right ) \left (2 \ln \relax (x ) c_{1}+\sqrt {2}\right )+\left (\sqrt {2}\, c_{1}-2 \ln \relax (x )\right ) \cos \left (\ln \relax (x ) \sqrt {2}\right )}\]