2.756   ODE No. 756

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

\[ y'(x)=\frac {x^6+2 x^3 y(x)+x^2 y(x)^2+y(x)^3}{x^4} \] Mathematica : cpu = 0.10973 (sec), leaf count = 93

\[\text {Solve}\left [87 \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {x^2+3 y(x)}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^6}} x^4}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]+9 c_1+29^{2/3} \left (\frac {1}{x^6}\right )^{2/3} x^5=0,y(x)\right ]\]

Maple : cpu = 0.036 (sec), leaf count = 37

\[ \left \{ y \left ( x \right ) ={\frac { \left ( -3+29\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) \right ) {x}^{2}}{9}} \right \} \]