\[ y''(x)=-\frac {b y(x)}{x^2 (x-a)^2} \] ✓ Mathematica : cpu = 0.203936 (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 = 0.194 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) =\sqrt {x \left ( a-x \right ) } \left ( \left ( {\frac {x}{a-x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}}{\it \_C2}+ \left ( {\frac {a-x}{x}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}-4\,b}}}{\it \_C1} \right ) \right \} \]