\[ y''(x) \left (a x^2+b \lambda +c\right )+y(x) \left (a x^2+\beta \lambda +\gamma \right )+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 80.1908 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (a \unicode {f817}^2+\beta \lambda +\gamma \right ) \unicode {f818}(\unicode {f817})+\left (a \unicode {f817}^2+c+b \lambda \right ) \unicode {f818}''(\unicode {f817})+\unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \}\right )(x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ \left ( a{x}^{2}+\beta \,\lambda +\gamma \right ) {\it \_Y} \left ( x \right ) + \left ( a{x}^{2}+b\lambda +c \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]