2.681   ODE No. 681

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

\[ y'(x)=\frac {a x^2 y(x)^2+a x y(x)^2+a x y(x)^2 \log \left (\frac {1}{x}\right )+b x^4+b x^3+b x^3 \log \left (\frac {1}{x}\right )+y(x)}{x} \] Mathematica : cpu = 0.0398627 (sec), leaf count = 84

\[\left \{\left \{y(x)\to \frac {\sqrt {b} x \tan \left (\frac {1}{12} \left (12 \sqrt {a} \sqrt {b} c_1+4 \sqrt {a} \sqrt {b} x^3+9 \sqrt {a} \sqrt {b} x^2-6 \sqrt {a} \sqrt {b} x^2 \log (x)\right )\right )}{\sqrt {a}}\right \}\right \}\]

Maple : cpu = 0.051 (sec), leaf count = 57

\[ \left \{ y \left ( x \right ) ={\frac {x}{a}\tan \left ( {\frac {{x}^{2}\ln \left ( {x}^{-1} \right ) }{2}\sqrt {ab}}+{\frac {{x}^{3}}{3}\sqrt {ab}}+{\frac {3\,{x}^{2}}{4}\sqrt {ab}}+{\it \_C1}\,\sqrt {ab} \right ) \sqrt {ab}} \right \} \]