2.1518   ODE No. 1518

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

\[ x \left (x^2+1\right ) y^{(3)}(x)+3 \left (2 x^2+1\right ) y''(x)-12 y(x)=0 \] Mathematica : cpu = 0.257157 (sec), leaf count = 106

\[\left \{\left \{y(x)\to \frac {1}{3} c_1 \left (2 x^2+1\right )+\frac {1}{3} c_2 x \sqrt {x^2+1}+\frac {c_3 \left (2 x^2+1\right ) \left (3 x^2+3 \sqrt {x^2+1} x^2 \log (x)-3 \sqrt {x^2+1} x^2 \log \left (\sqrt {x^2+1}+1\right )+1\right )}{6 \left (2 x^3+x\right )}\right \}\right \}\]

Maple : cpu = 0.48 (sec), leaf count = 56

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{x}^{2}+1}x+{\frac {{\it \_C2}}{x} \left ( 3\,\sqrt {{x}^{2}+1}{x}^{2}{\it Artanh} \left ( {\frac {1}{\sqrt {{x}^{2}+1}}} \right ) -3\,{x}^{2}-1 \right ) }+{\it \_C3}\, \left ( 2\,{x}^{2}+1 \right ) \right \} \]