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 = 0.850243 (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 = 0.279 (sec), leaf count = 62

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