\[ 6 y'(x) (a k+b x)+3 (2 a x+k) y''(x)+y(x) (3 b k+2 c x)+2 x y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 61.8649 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(2 \unicode {f817} c+3 b k) \unicode {f818}(\unicode {f817})+(6 \unicode {f817} b+6 a k) \unicode {f818}'(\unicode {f817})+(6 \unicode {f817} a+3 k) \unicode {f818}''(\unicode {f817})+2 \unicode {f817} \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ \left ( 3\,bk+2\,cx \right ) {\it \_Y} \left ( x \right ) + \left ( 6\,ak+6\,bx \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( 6\,ax+3\,k \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +2\,x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]