\[ \boxed { {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -3\, \left ( p+q \right ) x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,p \left ( 3\,q+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{x}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.499063 (sec), leaf count = 135 \[ \left \{\left \{y(x)\to c_1 \, _0F_2\left (;\frac {2}{3}-p,\frac {1}{3}-q;\frac {x^3}{27}\right )+c_2 (-1)^{\frac {1}{3} (3 p+1)} 3^{-3 p-1} x^{3 p+1} \, _0F_2\left (;p+\frac {4}{3},p-q+\frac {2}{3};\frac {x^3}{27}\right )+c_3 (-1)^{\frac {1}{3} (3 q+2)} 3^{-3 q-2} x^{3 q+2} \, _0F_2\left (;q+\frac {5}{3},-p+q+\frac {4}{3};\frac {x^3}{27}\right )\right \}\right \} \]
Maple: cpu = 0.203 (sec), leaf count = 77 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_0$F$_2$}(\ ;\,-q+{\frac {1}{3}},-p+{\frac {2}{3}};\,{\frac {{x}^{3}}{27}})} +{\it \_C2}\,{x}^{1+3\,p} {\mbox {$_0$F$_2$}(\ ;\,p+{\frac {4}{3}},-q+{\frac {2}{3}}+p;\,{\frac {{x}^{3}}{27}})} +{\it \_C3}\,{x}^{3\,q+2} {\mbox {$_0$F$_2$}(\ ;\,q+{\frac {5}{3}},q+{\frac {4}{3}}-p;\,{\frac {{x}^{3}}{27}})} \right \} \]