\[ (x-a)^3 (x-b)^3 y^{(3)}(x)-c y(x)=0 \] ✗ Mathematica : cpu = 135.25 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(a-\unicode {f817})^3 (b-\unicode {f817})^3 \unicode {f818}^{(3)}(\unicode {f817})-c \unicode {f818}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.612 (sec), leaf count = 437
\[ \left \{ y \left ( x \right ) = \left ( x-a \right ) ^{-2\,{\frac {b}{a-b}}} \left ( x-b \right ) ^{2\,{\frac {a}{a-b}}} \left ( \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=1 \right ) }{a-b}}}{\it \_C1}+ \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=3 \right ) }{a-b}}}{\it \_C3}+ \left ( b-x \right ) ^{-{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a-b}}} \left ( a-x \right ) ^{{\frac {{\it RootOf} \left ( {{\it \_Z}}^{3}+ \left ( -3\,a-3\,b \right ) {{\it \_Z}}^{2}+ \left ( 2\,{a}^{2}+8\,ab+2\,{b}^{2} \right ) {\it \_Z}-4\,{a}^{2}b-4\,a{b}^{2}-c,{\it index}=2 \right ) }{a-b}}}{\it \_C2} \right ) \right \} \]