\[ \boxed { {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\, \left ( 1-a \right ) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 4\,{b}^{2}{c}^{2}{x}^{2\,c+1}+1-4\,{\nu }^{2}{c}^{2}+3\,a \left ( a-1 \right ) x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\,{b}^{2}{c}^{2} \left ( c-a \right ) {x}^{2\,c}+a \left ( 4\,{\nu }^{2}{c}^{2}-{a}^{2} \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.121015 (sec), leaf count = 104 \[ \text {DSolve}\left [y(x) \left (a \left (4 c^2 \nu ^2-a^2\right )+4 b^2 c^2 (c-a) x^{2 c}\right )+y'(x) \left (3 (a-1) a x+4 b^2 c^2 x^{2 c+1}-4 c^2 \nu ^2+1\right )+3 (1-a) x^2 y''(x)+x^3 y^{(3)}(x)=0,y(x),x\right ] \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]