2.1518   ODE No. 1518

\[ x \left (x^2+1\right ) y^{(3)}(x)+3 \left (2 x^2+1\right ) y''(x)-12 y(x)=0 \] Mathematica : cpu = 0.229447 (sec), leaf count = 104


\[\left \{\left \{y(x)\to \frac {1}{3} c_1 \left (2 x^2+1\right )+\frac {1}{3} c_2 x \sqrt {x^2+1}-\frac {c_3 \left (2 x^2+1\right ) \left (3 \left (x^4+x^2\right ) \tanh ^{-1}\left (\sqrt {x^2+1}\right )-\sqrt {x^2+1} \left (3 x^2+1\right )\right )}{6 \sqrt {x^2+1} \left (2 x^3+x\right )}\right \}\right \}\] Maple : cpu = 0.341 (sec), leaf count = 60


\[y \relax (x ) = \frac {3 \arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right ) \sqrt {x^{2}+1}\, c_{2} x^{2}+c_{1} x^{2} \sqrt {x^{2}+1}+2 x^{3} c_{3}-3 x^{2} c_{2}+c_{3} x -c_{2}}{x}\]