\[ y''(x)=\frac {y'(x) \left (2 (a-1) x^2-2 a+2 b c \left (x^2-1\right ) x^c\right )}{x \left (x^2-1\right )}-\frac {y(x) \left (b c (2 a-c-1) x^{c+2}-b c (2 a-c+1) x^c+x^2 ((a-1) a-v (v+1))-a (a+1)+b^2 c^2 \left (x^2-1\right ) x^{2 c}\right )}{x^2 \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.108569 (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 = 0.1 (sec), leaf count = 25
\[y \relax (x ) = {\mathrm e}^{b \,x^{c}} x^{a} \left (c_{1} \LegendreP \left (v , x\right )+c_{2} \LegendreQ \left (v , x\right )\right )\]