\[ y''(x)=\frac {c y(x)}{(x-a)^2 (x-b)^2} \] ✓ Mathematica : cpu = 0.480511 (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 = 0.303 (sec), leaf count = 104
\[ \left \{ y \left ( x \right ) =\sqrt { \left ( a-x \right ) \left ( b-x \right ) } \left ( \left ( {\frac {a-x}{b-x}} \right ) ^{{\frac {1}{2\,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}}{\it \_C1}+ \left ( {\frac {a-x}{b-x}} \right ) ^{-{\frac {1}{2\,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}}{\it \_C2} \right ) \right \} \]