\[ \boxed { {x}^{4}{\it d4y} \left ( x \right ) +8\,{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +12\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.157020 (sec), leaf count = 378 \[ \left \{\left \{y(x)\to c_1 b^{\frac {a-c \mu -c \nu }{c}} \left (x^{2 c}\right )^{\frac {a-c \mu -c \nu }{2 c}} \, _2F_3\left (-\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}-\frac {\nu }{2}+1;1-\mu ,1-\nu ,-\mu -\nu +1;-b^2 x^{2 c}\right )+c_2 b^{\frac {a+c \mu -c \nu }{c}} \left (x^{2 c}\right )^{\frac {a+c \mu -c \nu }{2 c}} \, _2F_3\left (\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}-\frac {\nu }{2}+1;\mu +1,1-\nu ,\mu -\nu +1;-b^2 x^{2 c}\right )+c_3 b^{\frac {a-c \mu +c \nu }{c}} \left (x^{2 c}\right )^{\frac {a-c \mu +c \nu }{2 c}} \, _2F_3\left (-\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}+\frac {\nu }{2}+1;1-\mu ,\nu +1,-\mu +\nu +1;-b^2 x^{2 c}\right )+c_4 b^{\frac {a+c \mu +c \nu }{c}} \left (x^{2 c}\right )^{\frac {a+c \mu +c \nu }{2 c}} \, _2F_3\left (\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}+\frac {\nu }{2}+1;\mu +1,\nu +1,\mu +\nu +1;-b^2 x^{2 c}\right )\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 89 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {1}{2}}-{\frac { 1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C2}\,{x}^{-{\frac {1}{2}}+{ \frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C3}\,{x}^{-{\frac {1}{2} }-{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}}+{\it \_C4}\,{x}^{-{\frac {1} {2}}+{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}} \right \} \]