\[ y''(x)=\frac {c y(x)}{(x-a)^2 (x-b)^2} \] ✓ Mathematica : cpu = 0.792776 (sec), leaf count = 141
\[\left \{\left \{y(x)\to (x-a)^{\frac {1}{2} \left (1-\sqrt {\frac {4 c}{(a-b)^2}+1}\right )} (x-b)^{\frac {1}{2} \left (1-\sqrt {\frac {4 c}{(a-b)^2}+1}\right )} \left (c_1 (x-a)^{\sqrt {\frac {4 c}{(a-b)^2}+1}}-\frac {c_2 (x-b)^{\sqrt {\frac {4 c}{(a-b)^2}+1}}}{(a-b) \sqrt {\frac {4 c}{(a-b)^2}+1}}\right )\right \}\right \}\]
✓ Maple : cpu = 0.141 (sec), leaf count = 104
\[ \left \{ y \left ( x \right ) =\sqrt { \left ( a-x \right ) \left ( b-x \right ) } \left ( \left ( {\frac {a-x}{b-x}} \right ) ^{{\frac {1}{2\,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}}{\it \_C1}+ \left ( {\frac {a-x}{b-x}} \right ) ^{-{\frac {1}{2\,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}}{\it \_C2} \right ) \right \} \]