3.681   ODE No. 681

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) +{x}^{3}b\ln \left ( {x}^{-1} \right ) +{x}^{4}b+b{x}^{3}+xa \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( {x}^{-1} \right ) +a{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ax \left ( y \left ( x \right ) \right ) ^{2}}{x}}=0} \]

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

Mathematica: cpu = 0.045006 (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 = 0.031 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) ={\frac {x}{a}\tan \left ( {\frac {{x}^{2} \ln \left ( {x}^{-1} \right ) }{2}\sqrt {ab}}+{\frac {{x}^{3}}{3}\sqrt {ab}}+{\frac {3\,{x}^{2}}{4}\sqrt {ab}}+{\it \_C1}\,\sqrt {ab} \right ) \sqrt {ab}} \right \} \]