2.1517   ODE No. 1517

\[ x^3 y^{(3)}(x)-2 x^3+x^2 y''(x)+2 x y'(x)-y(x)+\log (x)=0 \] Mathematica : cpu = 0.257549 (sec), leaf count = 30686


\[ \text {Too large to display} \] Maple : cpu = 0.387 (sec), leaf count = 866


\[y \relax (x ) = -\left (\int -\frac {x^{\frac {\left (11-3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{600}+\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{6}+\frac {4}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \left (\cos ^{2}\left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )+\sin ^{2}\left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )\right ) \left (-\ln \relax (x )+2 x^{3}\right ) \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {3}\, \sqrt {23}}{13800 x^{3}}d x \right ) x^{\frac {\left (-11+3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{600}-\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{6}+\frac {2}{3}}+x^{\frac {\left (11-3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{1200}+\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \left (\int -\frac {x^{\frac {\left (-11+3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{600}-\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{6}+\frac {2}{3}} \left (x^{3}-\frac {\ln \relax (x )}{2}\right ) x^{\frac {\left (11-3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{1200}+\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (\sqrt {3}\, \left (\frac {100}{3}+\left (\sqrt {69}-\frac {11}{3}\right ) \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}\right ) \cos \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )-3 \left (-\frac {100}{3}+\left (\sqrt {69}-\frac {11}{3}\right ) \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}\right ) \sin \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )\right ) \sqrt {23}}{2300 x^{3}}d x +c_{2}\right ) \cos \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )+x^{\frac {\left (11-3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{1200}+\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \left (\int -\frac {3 \left (\left (-\frac {100}{3}+\left (\sqrt {69}-\frac {11}{3}\right ) \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}\right ) \cos \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )+\frac {\sin \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right ) \sqrt {3}\, \left (\frac {100}{3}+\left (\sqrt {69}-\frac {11}{3}\right ) \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}\right )}{3}\right ) x^{\frac {\left (-11+3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{600}-\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{6}+\frac {2}{3}} \left (x^{3}-\frac {\ln \relax (x )}{2}\right ) x^{\frac {\left (11-3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{1200}+\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {23}}{2300 x^{3}}d x +c_{3}\right ) \sin \left (\frac {\sqrt {3}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}} \left (3 \sqrt {69}\, \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}-11 \left (44+12 \sqrt {69}\right )^{\frac {1}{3}}+100\right ) \ln \relax (x )}{1200}\right )+c_{1} x^{\frac {\left (-11+3 \sqrt {69}\right ) \left (44+12 \sqrt {69}\right )^{\frac {2}{3}}}{600}-\frac {\left (44+12 \sqrt {69}\right )^{\frac {1}{3}}}{6}+\frac {2}{3}}\]