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 = 0.454191 (sec), leaf count = 104

DSolve[-12*y[x] + 3*(1 + 2*x^2)*Derivative[2][y][x] + x*(1 + x^2)*Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{3} c_1 \left (2 x^2+1\right )+\frac {1}{3} c_2 x \sqrt {x^2+1}-\frac {c_3 \left (2 x^2+1\right ) \left (3 \left (x^4+x^2\right ) \tanh ^{-1}\left (\sqrt {x^2+1}\right )-\sqrt {x^2+1} \left (3 x^2+1\right )\right )}{6 \sqrt {x^2+1} \left (2 x^3+x\right )}\right \}\right \}\]

✓ Maple : cpu = 0.415 (sec), leaf count = 60

dsolve((x^2+1)*x*diff(diff(diff(y(x),x),x),x)+3*(2*x^2+1)*diff(diff(y(x),x),x)-12*y(x)=0,y(x))
 

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