\[ \boxed { 2\,x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\, \left ( 2\,ax+k \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +6\, \left ( ak+bx \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 3\,bk+2\,cx \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 63.307539 (sec), leaf count = 80 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(2 \unicode {f817} c+3 b k) \unicode {f818}(\unicode {f817})+(6 \unicode {f817} b+6 a k) \unicode {f818}'(\unicode {f817})+(6 \unicode {f817} a+3 k) \unicode {f818}''(\unicode {f817})+2 \unicode {f817} \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.296 (sec), leaf count = 62 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ \left ( 3\,bk +2\,cx \right ) {\it \_Y} \left ( x \right ) + \left ( 6\,ak+6\,bx \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( 6\,ax+3\,k \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +2\,x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]