\[ (a+b) y''(x)-a y(x)-x y'(x)+x y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.107806 (sec), leaf count = 153
\[\left \{\left \{y(x)\to c_3 \left (\frac {i}{2}\right )^{-a-b+2} x^{-a-b+2} \, _1F_2\left (1-\frac {b}{2};-\frac {a}{2}-\frac {b}{2}+\frac {3}{2},-\frac {a}{2}-\frac {b}{2}+2;\frac {x^2}{4}\right )+\frac {1}{2} i c_2 x \, _1F_2\left (\frac {a}{2}+\frac {1}{2};\frac {3}{2},\frac {a}{2}+\frac {b}{2}+\frac {1}{2};\frac {x^2}{4}\right )+c_1 \, _1F_2\left (\frac {a}{2};\frac {1}{2},\frac {a}{2}+\frac {b}{2};\frac {x^2}{4}\right )\right \}\right \}\] ✓ Maple : cpu = 0.209 (sec), leaf count = 92
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_1$F$_2$}({\frac {a}{2}};\,{\frac {1}{2}},{\frac {a}{2}}+{\frac {b}{2}};\,{\frac {{x}^{2}}{4}})}+{\it \_C2}\,x{\mbox {$_1$F$_2$}({\frac {1}{2}}+{\frac {a}{2}};\,{\frac {3}{2}},{\frac {a}{2}}+{\frac {b}{2}}+{\frac {1}{2}};\,{\frac {{x}^{2}}{4}})}+{\it \_C3}\,{x}^{-a-b+2}{\mbox {$_1$F$_2$}(1-{\frac {b}{2}};\,2-{\frac {b}{2}}-{\frac {a}{2}},-{\frac {a}{2}}-{\frac {b}{2}}+{\frac {3}{2}};\,{\frac {{x}^{2}}{4}})} \right \} \]