\[ y''(x)=\frac {c y(x)}{(x-a)^2 (x-b)^2} \] ✓ Mathematica : cpu = 0.409161 (sec), leaf count = 154
DSolve[Derivative[2][y][x] == (c*y[x])/((-a + x)^2*(-b + x)^2),y[x],x]
\[\left \{\left \{y(x)\to c_1 (x-a)^{\frac {1}{2} \left (\sqrt {\frac {4 c}{(a-b)^2}+1}+1\right )} (x-b)^{\frac {1}{2} \left (1-\sqrt {\frac {4 c}{(a-b)^2}+1}\right )}-\frac {c_2 (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {\frac {4 c}{(a-b)^2}+1}} (x-b)^{\frac {1}{2} \sqrt {\frac {4 c}{(a-b)^2}+1}+\frac {1}{2}}}{(a-b) \sqrt {\frac {4 c}{(a-b)^2}+1}}\right \}\right \}\] ✓ Maple : cpu = 0.12 (sec), leaf count = 104
dsolve(diff(diff(y(x),x),x) = c/(x-a)^2/(x-b)^2*y(x),y(x))
\[y \left (x \right ) = \sqrt {\left (a -x \right ) \left (b -x \right )}\, \left (\left (\frac {a -x}{b -x}\right )^{\frac {\sqrt {a^{2}-2 a b +b^{2}+4 c}}{2 a -2 b}} c_{1}+\left (\frac {a -x}{b -x}\right )^{-\frac {\sqrt {a^{2}-2 a b +b^{2}+4 c}}{2 a -2 b}} c_{2}\right )\]