\[ y''(x)=-\frac {b y(x)}{x^2 (x-a)^2} \] ✓ Mathematica : cpu = 0.178819 (sec), leaf count = 132
DSolve[Derivative[2][y][x] == -((b*y[x])/(x^2*(-a + x)^2)),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 (x-a)^{\frac {1}{2} \sqrt {\frac {a^2-4 b}{a^2}}+\frac {1}{2}} x^{\frac {1}{2}-\frac {1}{2} \sqrt {\frac {a^2-4 b}{a^2}}}}{a \sqrt {\frac {a^2-4 b}{a^2}}}+c_1 (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}} x^{\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}+\frac {1}{2}}\right \}\right \}\] ✓ Maple : cpu = 0.076 (sec), leaf count = 67
dsolve(diff(diff(y(x),x),x) = -b/x^2/(x-a)^2*y(x),y(x))
\[y \left (x \right ) = \sqrt {x \left (a -x \right )}\, \left (\left (\frac {x}{a -x}\right )^{\frac {\sqrt {a^{2}-4 b}}{2 a}} c_{2}+\left (\frac {a -x}{x}\right )^{\frac {\sqrt {a^{2}-4 b}}{2 a}} c_{1}\right )\]