\[ y(x) \left (\left (a^2-c^2 \nu ^2\right ) \left (a^2+4 a c-c^2 \nu ^2+4 c^2\right )-b^4 c^4 x^{4 c}\right )+x^2 \left (2 a^2+4 (a+c-1)^2+4 (a-1) (c-1)-2 c^2 \nu ^2-1\right ) y''(x)+x (2 a+2 c-1) \left (-2 a^2-(2 a-1) (2 c-1)+2 c^2 \nu ^2\right ) y'(x)+x^3 (-4 a-4 c+6) y^{(3)}(x)+x^4 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.150844 (sec), leaf count = 213
\[\left \{\left \{y(x)\to b^{a/c} (-1)^{\frac {a-c \nu }{4 c}} 2^{-\frac {2 a}{c}-\nu -3} \left (x^{4 c}\right )^{\frac {a}{4 c}} \left (4^{\nu } \left (4 c_1 \Gamma (1-\nu )-i c_2 \Gamma (2-\nu )\right ) J_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )+4^{\nu } \left (4 c_1 \Gamma (1-\nu )+i c_2 \Gamma (2-\nu )\right ) I_{-\nu }\left (b \sqrt [4]{x^{4 c}}\right )+i^{\nu } \left (\left (4 c_3 \Gamma (\nu +1)-i c_4 \Gamma (\nu +2)\right ) J_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )+\left (4 c_3 \Gamma (\nu +1)+i c_4 \Gamma (\nu +2)\right ) I_{\nu }\left (b \sqrt [4]{x^{4 c}}\right )\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.112 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) ={x}^{a} \left ( {{\sl Y}_{\nu }\left (ib{x}^{c}\right )}{\it \_C4}+{{\sl Y}_{\nu }\left (b{x}^{c}\right )}{\it \_C2}+{{\sl J}_{\nu }\left (ib{x}^{c}\right )}{\it \_C3}+{{\sl J}_{\nu }\left (b{x}^{c}\right )}{\it \_C1} \right ) \right \} \]