2.629   ODE No. 629

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x)=\frac {(2 y(x) \log (x)-1)^2}{x} \] Mathematica : cpu = 0.665909 (sec), leaf count = 38

\[\left \{\left \{y(x)\to \frac {1}{\sqrt {2} \left (\sqrt {2} \log (x)-\tan \left (\frac {c_1+2 \log (x)}{\sqrt {2}}\right )\right )}\right \}\right \}\]

Maple : cpu = 20.097 (sec), leaf count = 62

\[ \left \{ y \left ( x \right ) ={\frac {\sin \left ( \sqrt {2}\ln \left ( x \right ) \right ) {\it \_C1}-\cos \left ( \sqrt {2}\ln \left ( x \right ) \right ) }{\sin \left ( \sqrt {2}\ln \left ( x \right ) \right ) \left ( 2\,{\it \_C1}\,\ln \left ( x \right ) +\sqrt {2} \right ) + \left ( \sqrt {2}{\it \_C1}-2\,\ln \left ( x \right ) \right ) \cos \left ( \sqrt {2}\ln \left ( x \right ) \right ) }} \right \} \]