\[ (2 a x+b) y'(x)+a y(x)+2 (x-1) x y^{(3)}(x)+3 (2 x-1) y''(x)=0 \] ✗ Mathematica : cpu = 62.2056 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{a \unicode {f818}(\unicode {f817})+(2 \unicode {f817} a+b) \unicode {f818}'(\unicode {f817})+(6 \unicode {f817}-3) \unicode {f818}''(\unicode {f817})+2 (\unicode {f817}-1) \unicode {f817} \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2,\unicode {f818}''(2)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.151 (sec), leaf count = 79
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\it MathieuC} \left ( -{\frac {a}{2}}-{\frac {b}{2}}+1,{\frac {a}{4}},\arccos \left ( \sqrt {x} \right ) \right ) \right ) ^{2}+{\it \_C2}\, \left ( {\it MathieuS} \left ( -{\frac {a}{2}}-{\frac {b}{2}}+1,{\frac {a}{4}},\arccos \left ( \sqrt {x} \right ) \right ) \right ) ^{2}+{\it \_C3}\,{\it MathieuC} \left ( -{\frac {a}{2}}-{\frac {b}{2}}+1,{\frac {a}{4}},\arccos \left ( \sqrt {x} \right ) \right ) {\it MathieuS} \left ( -{\frac {a}{2}}-{\frac {b}{2}}+1,{\frac {a}{4}},\arccos \left ( \sqrt {x} \right ) \right ) \right \} \]