\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac {cy \left ( x \right ) }{ \left ( x-a \right ) ^{2} \left ( x-b \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.699089 (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 = 0.078 (sec), leaf count = 116 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt { \left ( a-x \right ) \left ( b-x \right ) } \left ( {\frac {a-x}{b-x}} \right ) ^{{\frac {1}{2 \,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}}+{\it \_C2}\,\sqrt { \left ( a-x \right ) \left ( b-x \right ) } \left ( {\frac {a-x}{b-x}} \right ) ^{-{\frac {1}{2\,a-2\,b}\sqrt {{a}^{2}-2\,ab+{b}^{2}+4\,c}}} \right \} \]