3.854   ODE No. 854

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( \ln \left ( x \right ) +\ln \left ( y \left ( x \right ) \right ) -1+{x}^{2} \left ( \ln \left ( x \right ) \right ) ^{2}+2\,{x}^{2}\ln \left ( y \left ( x \right ) \right ) \ln \left ( x \right ) +{x}^{2} \left ( \ln \left ( y \left ( x \right ) \right ) \right ) ^{2} \right ) }{x}}=0} \]

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

Mathematica: cpu = 0.623579 (sec), leaf count = 49 \[ \text {DSolve}\left [y'(x)=\frac {y(x) \left (x^2 \log ^2(y(x))+2 x^2 \log (x) \log (y(x))+x^2 \log ^2(x)+\log (y(x))+\log (x)-1\right )}{x},y(x),x\right ] \]

Maple: cpu = 0.156 (sec), leaf count = 51 \[ \left \{ y \left ( x \right ) ={1 \left ( {x}^{{\frac {{x}^{3}}{{x}^{3}+3 \,{\it \_C1}}}} \right ) ^{-1} \left ( {x}^{{\frac {{\it \_C1}}{{x}^{3}+ 3\,{\it \_C1}}}} \right ) ^{-3} \left ( {{\rm e}^{{\frac {x}{{x}^{3}+3\, {\it \_C1}}}}} \right ) ^{-3}} \right \} \]