\[ y''(x)=c-\frac {b y(x)}{x^2 (x-a)^2} \] ✓ Mathematica : cpu = 0.814882 (sec), leaf count = 371
\[\left \{\left \{y(x)\to \frac {a c x^2 (a-x) \left (1-\frac {x}{a}\right )^{-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}-\frac {1}{2}} \left (\left (\sqrt {1-\frac {4 b}{a^2}}-3\right ) \left (1-\frac {x}{a}\right )^{\sqrt {1-\frac {4 b}{a^2}}} \, _2F_1\left (\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}-\frac {1}{2},\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {3}{2};\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {5}{2};\frac {x}{a}\right )+\left (\sqrt {1-\frac {4 b}{a^2}}+3\right ) \, _2F_1\left (-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}-\frac {1}{2},\frac {3}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}};\frac {5}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}};\frac {x}{a}\right )\right )}{2 \left (2 a^2+b\right ) \sqrt {1-\frac {4 b}{a^2}}}+c_1 x^{\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {1}{2}} (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}}+\frac {c_2 x^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}} (x-a)^{\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {1}{2}}}{a \sqrt {1-\frac {4 b}{a^2}}}\right \}\right \}\]
✓ Maple : cpu = 0.204 (sec), leaf count = 175
\[ \left \{ y \left ( x \right ) ={1 \left ( \left ( {\it \_C2}\,\sqrt {{a}^{2}-4\,b}-\int \!\sqrt {x \left ( a-x \right ) } \left ( {\frac {a-x}{x}} \right ) ^{-{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}}\,{\rm d}xc \right ) \left ( {\frac {a-x}{x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}}+ \left ( \int \!\sqrt {x \left ( a-x \right ) } \left ( {\frac {x}{a-x}} \right ) ^{-{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}}\,{\rm d}xc+{\it \_C1}\,\sqrt {{a}^{2}-4\,b} \right ) \left ( {\frac {x}{a-x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}} \right ) \sqrt {x \left ( a-x \right ) }{\frac {1}{\sqrt {{a}^{2}-4\,b}}}} \right \} \]