2.704   ODE No. 704

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

\[ y'(x)=\frac {2 a x^3 y(x)^2+2 b x^5-y(x)+x y(x) \log (x)}{x (x \log (x)-1)} \] Mathematica : cpu = 8.18556 (sec), leaf count = 66

\[\left \{\left \{y(x)\to \frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} \int _1^x\frac {2 K[1]^3}{K[1] \log (K[1])-1}dK[1]+\sqrt {a} \sqrt {b} c_1\right )}{\sqrt {a}}\right \}\right \}\] Maple : cpu = 0.283 (sec), leaf count = 38

\[ \left \{ y \left ( x \right ) ={\frac {x}{a}\tan \left ( 2\,\sqrt {ab} \left ( {\it \_C1}+\int \!{\frac {{x}^{3}}{x\ln \left ( x \right ) -1}}\,{\rm d}x \right ) \right ) \sqrt {ab}} \right \} \]