2.1517   ODE No. 1517

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

\[ x^2 y''(x)+x^3 y^{(3)}(x)-2 x^3+2 x y'(x)-y(x)+\log (x)=0 \] Mathematica : cpu = 0.27814 (sec), leaf count = 30686 \[ \text {Too large to display} \] Maple : cpu = 0.348 (sec), leaf count = 866

\[ \left \{ y \left ( x \right ) =-\int \!-{\frac { \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \left ( -\ln \left ( x \right ) +2\,{x}^{3} \right ) \left ( {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}} \right ) ^{2}\sqrt [3]{44+12\,\sqrt {69}}\sqrt {3}\sqrt {23}}{13800\,{x}^{3}} \left ( \left ( \cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \right ) ^{2}+ \left ( \sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \right ) ^{2} \right ) }\,{\rm d}x{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}}+ \left ( \int \!-{\frac {{x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}}\sqrt [3]{44+12\,\sqrt {69}}\sqrt {23}}{2300\,{x}^{3}} \left ( {x}^{3}-{\frac {\ln \left ( x \right ) }{2}} \right ) \left ( \sqrt {3} \left ( {\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) -3\, \left ( -{\frac {100}{3}}+ \left ( \sqrt {69}-11/3 \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \right ) }\,{\rm d}x+{\it \_C2} \right ) {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}\cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) + \left ( \int \!-{\frac {3\,{x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{2/3}}{1200}}+1/12\,\sqrt [3]{44+12\,\sqrt {69}}+2/3}{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{2/3}}{600}}-1/6\,\sqrt [3]{44+12\,\sqrt {69}}+2/3}\sqrt [3]{44+12\,\sqrt {69}}\sqrt {23}}{2300\,{x}^{3}} \left ( {x}^{3}-{\frac {\ln \left ( x \right ) }{2}} \right ) \left ( \left ( -{\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) +{\frac {\sqrt {3} \left ( {\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) }{3}\sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) } \right ) }\,{\rm d}x+{\it \_C3} \right ) {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}\sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) +{\it \_C1}\,{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}} \right \} \]