\[ y(x) \left (\left (a^2-c^2 \nu ^2\right ) \left (a^2+4 a c-c^2 \nu ^2+4 c^2\right )-b^4 c^4 x^{4 c}\right )+x^2 \left (2 a^2+4 (a+c-1)^2+4 (a-1) (c-1)-2 c^2 \nu ^2-1\right ) y''(x)+x (2 a+2 c-1) \left (-2 a^2-(2 a-1) (2 c-1)+2 c^2 \nu ^2\right ) y'(x)+x^3 (-4 a-4 c+6) y^{(3)}(x)+x^4 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.0989139 (sec), leaf count = 470
\[\left \{\left \{y(x)\to c_1 \Gamma (1-\nu ) (-1)^{\frac {a-c \nu }{4 c}} 2^{-\frac {2 (a-c \nu )}{c}-\nu -1} b^{\frac {a-c \nu }{c}+\nu } \left (x^{4 c}\right )^{\frac {a-c \nu }{4 c}+\frac {\nu }{4}} \left (J_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )+I_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )\right )+c_2 \Gamma (2-\nu ) (-1)^{\frac {a-c \nu +2 c}{4 c}} 2^{-\frac {2 (a-c \nu +2 c)}{c}-\nu +1} b^{\frac {a-c \nu +2 c}{c}+\nu -2} \left (x^{4 c}\right )^{\frac {a-c \nu +2 c}{4 c}+\frac {\nu -2}{4}} \left (I_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )-J_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )\right )+c_3 \Gamma (\nu +1) (-1)^{\frac {a+c \nu }{4 c}} 2^{-\frac {2 (a+c \nu )}{c}+\nu -1} b^{\frac {a+c \nu }{c}-\nu } \left (x^{4 c}\right )^{\frac {a+c \nu }{4 c}-\frac {\nu }{4}} \left (J_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )+I_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )\right )+c_4 \Gamma (\nu +2) (-1)^{\frac {a+c \nu +2 c}{4 c}} 2^{-\frac {2 (a+c \nu +2 c)}{c}+\nu +1} b^{\frac {a+c \nu +2 c}{c}-\nu -2} \left (x^{4 c}\right )^{\frac {a+c \nu +2 c}{4 c}+\frac {1}{4} (-\nu -2)} \left (I_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )-J_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.094 (sec), leaf count = 49
\[y \relax (x ) = x^{a} \left (\BesselY \left (\nu , i b \,x^{c}\right ) c_{4}+\BesselY \left (\nu , b \,x^{c}\right ) c_{2}+\BesselJ \left (\nu , i b \,x^{c}\right ) c_{3}+\BesselJ \left (\nu , b \,x^{c}\right ) c_{1}\right )\]