2.985   ODE No. 985

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

\[ y'(x)=\frac {(x y(x)+1) \left (x^2 y(x)^2+x^2 y(x)+x^2+2 x y(x)+x+1\right )}{x^5} \] Mathematica : cpu = 0.329032 (sec), leaf count = 103

\[\text {Solve}\left [-\frac {17}{3} \text {RootSum}\left [-17 \text {$\#$1}^3+3 \sqrt [3]{-34} \text {$\#$1}-17\& ,\frac {\log \left (\frac {\frac {3 y(x)}{x^2}+\frac {x+3}{x^3}}{\sqrt [3]{34} \sqrt [3]{-\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{-34}-17 \text {$\#$1}^2}\& \right ]=-\frac {1}{9} 34^{2/3} \left (-\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ]\] Maple : cpu = 0.15 (sec), leaf count = 43

\[ \left \{ y \left ( x \right ) ={\frac {17\,{\it RootOf} \left ( 162\,\int ^{{\it \_Z}}\! \left ( 289\,{{\it \_a}}^{3}+54\,{\it \_a}-54 \right ) ^{-1}{d{\it \_a}}x+3\,{\it \_C1}\,x+2 \right ) x-3\,x-9}{9\,x}} \right \} \]