2.854   ODE No. 854

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

\[ y'(x)=\frac {y(x) \left (x^2 \log ^2(y(x))+2 x^2 \log (x) \log (y(x))+x^2 \log ^2(x)+\log (y(x))+\log (x)-1\right )}{x} \] Mathematica : cpu = 0.894089 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == ((-1 + Log[x] + x^2*Log[x]^2 + Log[y[x]] + 2*x^2*Log[x]*Log[y[x]] + x^2*Log[y[x]]^2)*y[x])/x, y[x], x]

Maple : cpu = 0.941 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) ={ \left ( {x}^{{\frac {{x}^{3}}{{x}^{3}+3\,{\it \_C1}}}} \right ) ^{-1} \left ( {x}^{{\frac {{\it \_C1}}{{x}^{3}+3\,{\it \_C1}}}} \right ) ^{-3} \left ( {{\rm e}^{{\frac {x}{{x}^{3}+3\,{\it \_C1}}}}} \right ) ^{-3}} \right \} \]