\[ \boxed { {\it d4y} \left ( x \right ) +a \left ( bx-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +ab{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +\lambda \,y \left ( x \right ) =0} \]
Mathematica: cpu = 0.429555 (sec), leaf count = 67 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\lambda \unicode {f818}(\unicode {f817})+a b \unicode {f818}'(\unicode {f817})+a (\unicode {f817} b-1) \unicode {f818}''(\unicode {f817})+\unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ \lambda \,{ \it \_Y} \left ( x \right ) +ab{\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +a \left ( bx-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{ x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{4}}{{\rm d}{x}^{4 }}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]