\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( ap{x}^{b}+q \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( a{x}^{b}-1 \right ) }}-{\frac { \left ( ar{x}^{b}+s \right ) y \left ( x \right ) }{{x}^{2} \left ( a{x}^{b}-1 \right ) }}=0} \]
Mathematica: cpu = 0.132017 (sec), leaf count = 481 \[ \left \{\left \{y(x)\to c_1 i^{\frac {-\sqrt {q^2+2 q+4 s+1}+q+1}{b}} a^{\frac {-\sqrt {q^2+2 q+4 s+1}+q+1}{2 b}} \left (x^b\right )^{\frac {-\sqrt {q^2+2 q+4 s+1}+q+1}{2 b}} \, _2F_1\left (\frac {p}{2 b}+\frac {q}{2 b}-\frac {\sqrt {p^2-2 p-4 r+1}}{2 b}-\frac {\sqrt {q^2+2 q+4 s+1}}{2 b},\frac {p}{2 b}+\frac {q}{2 b}+\frac {\sqrt {p^2-2 p-4 r+1}}{2 b}-\frac {\sqrt {q^2+2 q+4 s+1}}{2 b};1-\frac {\sqrt {q^2+2 q+4 s+1}}{b};a x^b\right )+c_2 i^{\frac {\sqrt {q^2+2 q+4 s+1}+q+1}{b}} a^{\frac {\sqrt {q^2+2 q+4 s+1}+q+1}{2 b}} \left (x^b\right )^{\frac {\sqrt {q^2+2 q+4 s+1}+q+1}{2 b}} \, _2F_1\left (\frac {p}{2 b}+\frac {q}{2 b}-\frac {\sqrt {p^2-2 p-4 r+1}}{2 b}+\frac {\sqrt {q^2+2 q+4 s+1}}{2 b},\frac {p}{2 b}+\frac {q}{2 b}+\frac {\sqrt {p^2-2 p-4 r+1}}{2 b}+\frac {\sqrt {q^2+2 q+4 s+1}}{2 b};\frac {\sqrt {q^2+2 q+4 s+1}}{b}+1;a x^b\right )\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 253 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}({\frac {1}{2\,b} \left ( p+q+\sqrt {{q}^{2}+2\,q+4\,s+1}+\sqrt {{p}^{2}-2\,p-4\,r+1} \right ) },{\frac {1}{2\,b} \left ( p+q+\sqrt {{q}^{2}+2\,q+4\,s+1}-\sqrt {{p}^{2}-2\,p-4\,r+1} \right ) };\,{\frac {1}{b} \left ( b+\sqrt {{q}^{2}+2\,q+4\,s+1} \right ) };\,a{x}^{b})} {x}^{{\frac {q}{2}}+{\frac {1}{2}\sqrt {{q}^{2}+2\,q+4\,s+1}}+{\frac { 1}{2}}}+{\it \_C2}\, {\mbox {$_2$F$_1$}(-{\frac {1}{2\,b} \left ( -p-q+\sqrt {{q}^{2}+2\,q+4\,s+1}+\sqrt {{p}^{2}-2\,p-4\,r+1} \right ) },{\frac {1}{2\,b} \left ( p+q-\sqrt {{q}^{2}+2\,q+4\,s+1}+\sqrt {{p}^{2}-2\,p-4\,r+1} \right ) };\,{\frac {1}{b} \left ( b-\sqrt {{q}^{2}+2\,q+4\,s+1} \right ) };\,a{x}^{b})} {x}^{{\frac {q}{2}}-{\frac {1}{2}\sqrt {{q}^{2}+2\,q+4\,s+1}}+{\frac { 1}{2}}} \right \} \]