\[ y''(x)=\frac {c y(x)}{(x-a)^2 (x-b)^2} \] ✓ Mathematica : cpu = 0.467723 (sec), leaf count = 154
\[\left \{\left \{y(x)\to c_1 (x-a)^{\frac {1}{2} \left (\sqrt {\frac {4 c}{(a-b)^2}+1}+1\right )} (x-b)^{\frac {1}{2} \left (1-\sqrt {\frac {4 c}{(a-b)^2}+1}\right )}-\frac {c_2 (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {\frac {4 c}{(a-b)^2}+1}} (x-b)^{\frac {1}{2} \sqrt {\frac {4 c}{(a-b)^2}+1}+\frac {1}{2}}}{(a-b) \sqrt {\frac {4 c}{(a-b)^2}+1}}\right \}\right \}\] ✓ Maple : cpu = 0.13 (sec), leaf count = 104
\[\left \{y \left (x \right ) = \sqrt {\left (a -x \right ) \left (b -x \right )}\, \left (c_{1} \left (\frac {a -x}{b -x}\right )^{\frac {\sqrt {a^{2}-2 a b +b^{2}+4 c}}{2 a -2 b}}+c_{2} \left (\frac {a -x}{b -x}\right )^{-\frac {\sqrt {a^{2}-2 a b +b^{2}+4 c}}{2 a -2 b}}\right )\right \}\]