\[ \boxed { \left ( x-a \right ) ^{3} \left ( x-b \right ) ^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -cy \left ( x \right ) =0} \]
Mathematica: cpu = 135.354688 (sec), leaf count = 58 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(a-\unicode {f817})^3 (b-\unicode {f817})^3 \unicode {f818}^{(3)}(\unicode {f817})-c \unicode {f818}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.421 (sec), leaf count = 500 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-a \right ) ^{-2\,{ \frac {b}{a-b}}} \left ( x-b \right ) ^{2\,{\frac {a}{a-b}}} \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a- 3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,b{a}^{2}-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a -b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3} + \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2 \,{b}^{2} \right ) {\it \_Z}-4\,b{a}^{2}-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a-b}}}+{\it \_C2}\, \left ( x-a \right ) ^{-2\,{\frac {b}{a-b }}} \left ( x-b \right ) ^{2\,{\frac {a}{a-b}}} \left ( b-x \right ) ^{-{ \frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}- 4\,b{a}^{2}-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3 \,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,b{a}^{2}-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a -b}}}+{\it \_C3}\, \left ( x-a \right ) ^{-2\,{\frac {b}{a-b}}} \left ( x -b \right ) ^{2\,{\frac {a}{a-b}}} \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^ {2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,b{a}^{2}- 4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}} \left ( a-x \right ) ^{{ \frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}- 4\,b{a}^{2}-4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}} \right \} \]