\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac { \left ( 2\,bc{x}^{c} \left ( {x}^{2}-1 \right ) +2\, \left ( a-1 \right ) {x}^{2}-2\,a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( {x}^{2}-1 \right ) }}-{\frac { \left ( {b}^{2}{c}^{2}{x}^{2\,c} \left ( {x}^{2}-1 \right ) +bc{x}^{c+2} \left ( 2\,a-c-1 \right ) -bc{x}^{c} \left ( 2\,a-c+1 \right ) +{x}^{2} \left ( a \left ( a-1 \right ) -v \left ( v+1 \right ) \right ) -a \left ( a+1 \right ) \right ) y \left ( x \right ) }{{x}^{2} \left ( {x}^{2}-1 \right ) }}=0} \]
Mathematica: cpu = 0.171522 (sec), leaf count = 42 \[ \left \{\left \{y(x)\to c_1 P_v(x) e^{a \log (x)+b x^c}+c_2 Q_v(x) e^{a \log (x)+b x^c}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{a}{{\rm e}^{b{x}^{c}}}{ \it LegendreP} \left ( v,x \right ) +{\it \_C2}\,{x}^{a}{{\rm e}^{b{x}^{ c}}}{\it LegendreQ} \left ( v,x \right ) \right \} \]