\[ \boxed { {x}^{4}{\it d4y} \left ( x \right ) + \left ( 6-4\,a \right ) {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( 4\,{b}^{2}{c}^{2}{x}^{2\,c}+6\, \left ( a-1 \right ) ^{2}-2\,{c}^{2} \left ( {\mu }^{2}+{\nu }^{2} \right ) +1 \right ) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 4\, \left ( 3\,c-2\,a+1 \right ) {b}^{2}{c}^{2}{x}^{2\,c}+ \left ( 2\,a-1 \right ) \left ( 2\,{c}^{2} \left ( {\mu }^{2}+{\nu }^{2} \right ) -2\,a \left ( a-1 \right ) -1 \right ) \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\, \left ( a-c \right ) \left ( a-2\,c \right ) {b}^{2}{c}^{2}{x}^{2\,c}+ \left ( c\mu +c\nu +a \right ) \left ( c\mu +c\nu -a \right ) \left ( c\mu -c\nu +a \right ) \left ( c\mu -c\nu -a \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.152019 (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 = 0.218 (sec), leaf count = 81 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{a}{{\sl J}_{\mu }\left ({x }^{c}b\right )}{{\sl Y}_{\nu }\left ({x}^{c}b\right )}+{\it \_C2}\,{x}^{a} {{\sl J}_{\nu }\left ({x}^{c}b\right )}{{\sl J}_{\mu }\left ({x}^{c}b \right )}+{\it \_C3}\,{x}^{a}{{\sl J}_{\nu }\left ({x}^{c}b\right )}{ {\sl Y}_{\mu }\left ({x}^{c}b\right )}+{\it \_C4}\,{x}^{a}{{\sl Y}_{\nu }\left ({x}^{c}b\right )}{{\sl Y}_{\mu }\left ({x}^{c}b\right )} \right \} \]