3.994   ODE No. 994

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{x}^{3} \left ( - \left ( y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) \ln \left ( x \right ) - \left ( \ln \left ( x \right ) \right ) ^{2} \right ) +{\frac {y \left ( x \right ) }{x\ln \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 0.122515 (sec), leaf count = 198 \[ \left \{\left \{y(x)\to -\frac {c_1 e^{\frac {1}{16} x^4 (4 \log (x)-1)} \left (\frac {x^3}{4}+\frac {1}{4} x^3 (4 \log (x)-1)\right )+\frac {1}{16} x^4 e^{\frac {1}{16} x^4 (4 \log (x)-1)} (4 \log (x)-1) \left (\frac {x^3}{4}+\frac {1}{4} x^3 (4 \log (x)-1)\right )+\frac {1}{4} x^3 e^{\frac {1}{16} x^4 (4 \log (x)-1)}+\frac {1}{4} x^3 e^{\frac {1}{16} x^4 (4 \log (x)-1)} (4 \log (x)-1)}{x^3 \left (c_1 e^{\frac {1}{16} x^4 (4 \log (x)-1)}+\frac {1}{16} x^4 e^{\frac {1}{16} x^4 (4 \log (x)-1)} (4 \log (x)-1)\right )}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) =-{\frac {\ln \left ( x \right ) \left ( 4 \,{x}^{4}\ln \left ( x \right ) -{x}^{4}+8\,{\it \_C1}+16 \right ) }{4\, {x}^{4}\ln \left ( x \right ) -{x}^{4}+8\,{\it \_C1}}} \right \} \]