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

DSolve[-2*x^3 + Log[x] - y[x] + 2*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]
 

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

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)+ln(x)+2*x*diff(y(x),x)-y(x)-2*x^3=0,y(x))
 

\[y \left (x \right ) = -\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 \left (x \right )}{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 \left (x \right )}{1200}\right )\right ) \left (-\ln \left (x \right )+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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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 \left (x \right )}{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}}\]