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 = 0.699954 (sec), leaf count = 47

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

Maple : cpu = 0.201 (sec), leaf count = 72

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