\[ (x-a)^3 (x-b)^3 y^{(3)}(x)-c y(x)=0 \] ✓ Mathematica : cpu = 130.113 (sec), leaf count = 165
\[\left \{\left \{y(x)\to c_1 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,1\right ]}+c_2 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,2\right ]}+c_3 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,3\right ]}\right \}\right \}\] ✓ Maple : cpu = 0.611 (sec), leaf count = 437
\[ \left \{ y \left ( x \right ) = \left ( x-a \right ) ^{-2\,{\frac {b}{a-b}}} \left ( x-b \right ) ^{2\,{\frac {a}{a-b}}} \left ( \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a-b}}}{\it \_C1}+ \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a-b}}}{\it \_C2}+ \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}}{\it \_C3} \right ) \right \} \]