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 = 0.199371 (sec), leaf count = 95

\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 y(x)}{x^4}+\frac {1}{x^2}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^6}\right )^{2/3} x^5+c_1,y(x)\right ]\] Maple : cpu = 0.036 (sec), leaf count = 37

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