\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -a{x}^{b}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.019502 (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 = 0.093 (sec), leaf count = 114 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_0$F$_2$}(\ ;\,{\frac {b+2}{b+3}},{\frac {b+1}{b+3}};\,{\frac {{x}^{b+3}a}{ \left ( b+3 \right ) ^{3}}})} +{\it \_C2}\,x {\mbox {$_0$F$_2$}(\ ;\,{\frac {b+4}{b+3}},{\frac {b+2}{b+3}};\,{\frac {{x}^{b+3}a}{ \left ( b+3 \right ) ^{3}}})} +{\it \_C3}\,{x}^{2} {\mbox {$_0$F$_2$}(\ ;\,{\frac {b+5}{b+3}},{\frac {b+4}{b+3}};\,{\frac {{x}^{b+3}a}{ \left ( b+3 \right ) ^{3}}})} \right \} \]