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 = 0.989133 (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 = 0.251 (sec), leaf count = 62

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