\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( a \left ( b+2 \right ) {x}^{2}+ \left ( c-d+1 \right ) x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( ax+1 \right ) {x}^{2}}}-{\frac { \left ( abx-cd \right ) y \left ( x \right ) }{ \left ( ax+1 \right ) {x}^{2}}}=0} \]
Mathematica: cpu = 0.263533 (sec), leaf count = 66 \[ \left \{\left \{y(x)\to c_1 a^{-c} x^{-c} \, _2F_1(1-c,b-c;-c-d+1;-a x)+c_2 a^d x^d \, _2F_1(d+1,b+d;c+d+1;-a x)\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 89 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{d} \left ( ax+1 \right ) ^ {-b+c-d}{\mbox {$_2$F$_1$}(c,1-b+c;\,1+d+c;\,-ax)}+{\it \_C2}\,{x}^{-c} \left ( ax+1 \right ) ^{-b+c-d} {\mbox {$_2$F$_1$}(-d,1-b-d;\,1-d-c;\,-ax)} \right \} \]