\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {by \left ( x \right ) }{{x}^{2} \left ( x-a \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.297038 (sec), leaf count = 132 \[ \left \{\left \{y(x)\to \frac {c_2 (x-a)^{\frac {1}{2} \sqrt {\frac {a^2-4 b}{a^2}}+\frac {1}{2}} x^{\frac {1}{2}-\frac {1}{2} \sqrt {\frac {a^2-4 b}{a^2}}}}{a \sqrt {\frac {a^2-4 b}{a^2}}}+c_1 (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}} x^{\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {1}{2}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 75 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x \left ( a-x \right ) } \left ( {\frac {a-x}{x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b }}}+{\it \_C2}\,\sqrt {x \left ( a-x \right ) } \left ( {\frac {x}{a-x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}} \right \} \]