\[ y^{(3)}(x)-a x^b y(x)=0 \] ✓ Mathematica : cpu = 0.0146767 (sec), leaf count = 168
\[\left \{\left \{y(x)\to (-1)^{\frac {1}{b+3}} (b+3)^{-\frac {3}{b+3}} c_2 x a^{\frac {1}{b+3}} \, _0F_2\left (;1-\frac {1}{b+3},1+\frac {1}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )+(-1)^{\frac {2}{b+3}} (b+3)^{-\frac {6}{b+3}} c_3 x^2 a^{\frac {2}{b+3}} \, _0F_2\left (;1+\frac {1}{b+3},1+\frac {2}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )+c_1 \, _0F_2\left (;1-\frac {2}{b+3},1-\frac {1}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )\right \}\right \}\] ✓ Maple : cpu = 0.1 (sec), leaf count = 114
\[y \relax (x ) = c_{1} \hypergeom \left (\left [\right ], \left [\frac {b +1}{b +3}, \frac {b +2}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )+c_{2} x \hypergeom \left (\left [\right ], \left [\frac {b +2}{b +3}, \frac {b +4}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )+c_{3} x^{2} \hypergeom \left (\left [\right ], \left [\frac {b +5}{b +3}, \frac {b +4}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )\]