2.855   ODE No. 855

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

\[ y'(x)=\frac {y(x) \left (x^3 \log ^2(y(x))+2 x^3 \log (x) \log (y(x))+x^3 \log ^2(x)+\log (y(x))+\log (x)-1\right )}{x} \] Mathematica : cpu = 0.821865 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == ((-1 + Log[x] + x^3*Log[x]^2 + Log[y[x]] + 2*x^3*Log[x]*Log[y[x]] + x^3*Log[y[x]]^2)*y[x])/x, y[x], x]

Maple : cpu = 0.946 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) ={ \left ( {x}^{{\frac {{x}^{4}}{{x}^{4}+4\,{\it \_C1}}}} \right ) ^{-1} \left ( {x}^{{\frac {{\it \_C1}}{{x}^{4}+4\,{\it \_C1}}}} \right ) ^{-4} \left ( {{\rm e}^{{\frac {x}{{x}^{4}+4\,{\it \_C1}}}}} \right ) ^{-4}} \right \} \]