\[ (x-a)^5 (x-b)^5 y^{(5)}(x)-c y(x)=0 \] ✓ Mathematica : cpu = 271.105 (sec), leaf count = 331
\[\left \{\left \{y(x)\to c_1 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,1\right ]}+c_2 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,2\right ]}+c_3 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,3\right ]}+c_4 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,4\right ]}+c_5 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,5\right ]}\right \}\right \}\] ✓ Maple : cpu = 1.732 (sec), leaf count = 553
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left ({\mathrm e}^{c_{2}+\int -\frac {4 \left (\frac {\textit {\_f}}{4}+a +\left (-\frac {\textit {\_f}}{4}-b \right ) {\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}\right ) \textit {\_g} \left (\textit {\_f} \right )}{{\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}-1}d \textit {\_f}}, \left [\left \{\frac {-96 \left (\left (\frac {\textit {\_f}^{5}}{96}+a^{4} b +\frac {13 a^{3} b^{2}}{3}+\frac {13 a^{2} b^{3}}{3}+a \,b^{4}+\left (\frac {5 a}{48}+\frac {5 b}{48}\right ) \textit {\_f}^{4}+\left (\frac {35}{96} a^{2}+\frac {15}{16} a b +\frac {35}{96} b^{2}\right ) \textit {\_f}^{3}+\frac {25 \left (a +b \right ) \left (a^{2}+\frac {22}{5} a b +b^{2}\right ) \textit {\_f}^{2}}{48}+\left (\frac {1}{4} a^{4}+\frac {19}{6} a^{3} b +\frac {13}{2} a^{2} b^{2}+\frac {19}{6} a \,b^{3}+\frac {1}{4} b^{4}\right ) \textit {\_f} -\frac {c}{96}\right ) \textit {\_g} \left (\textit {\_f} \right )^{2}+\frac {5 \textit {\_f}}{32}+\frac {5 a}{16}+\frac {5 b}{16}+\frac {25 \left (\frac {\textit {\_f}}{2}+a +b \right ) \left (\frac {2 \textit {\_f}^{2}}{5}+a^{2}+\frac {22 a b}{5}+b^{2}+\left (\frac {8 a}{5}+\frac {8 b}{5}\right ) \textit {\_f} \right ) \textit {\_g} \left (\textit {\_f} \right )}{48}\right ) \textit {\_g} \left (\textit {\_f} \right )^{5}+35 \left (\left (\frac {2 \textit {\_f}^{2}}{7}+a^{2}+\frac {18 a b}{7}+b^{2}+\left (\frac {8 a}{7}+\frac {8 b}{7}\right ) \textit {\_f} \right ) \textit {\_g} \left (\textit {\_f} \right )+\frac {2}{7}\right ) \textit {\_g} \left (\textit {\_f} \right )^{3} \left (\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )\right )-30 \left (\frac {\textit {\_f}}{2}+a +b \right ) \textit {\_g} \left (\textit {\_f} \right )^{2} \left (\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )\right )^{2}+\textit {\_g} \left (\textit {\_f} \right )^{2} \left (\frac {d^{3}}{d \textit {\_f}^{3}}\textit {\_g} \left (\textit {\_f} \right )\right )+15 \left (\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )\right )^{3}+10 \left (\left (\frac {\textit {\_f}}{2}+a +b \right ) \textit {\_g} \left (\textit {\_f} \right )^{2}-\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )\right ) \textit {\_g} \left (\textit {\_f} \right ) \left (\frac {d^{2}}{d \textit {\_f}^{2}}\textit {\_g} \left (\textit {\_f} \right )\right )}{\textit {\_g} \left (\textit {\_f} \right )^{2}}=0\right \}, \left \{\textit {\_f} =\frac {-4 x y \left (x \right )+\left (a -x \right ) \left (b -x \right ) \left (\frac {d}{d x}y \left (x \right )\right )}{y \left (x \right )}, \textit {\_g} \left (\textit {\_f} \right )=\frac {y \left (x \right )^{2}}{\left (a -x \right ) \left (\left (a -x \right ) \left (b -x \right ) \left (\frac {d^{2}}{d x^{2}}y \left (x \right )\right ) y \left (x \right )-\left (a -x \right ) \left (b -x \right ) \left (\frac {d}{d x}y \left (x \right )\right )^{2}-\left (a +b -2 x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) y \left (x \right )-4 y \left (x \right )^{2}\right ) \left (b -x \right )}\right \}, \left \{x =\frac {b \,{\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}-a}{{\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}-1}, y \left (x \right )={\mathrm e}^{c_{2}+\int -\frac {4 \left (\frac {\textit {\_f}}{4}+a +\left (-\frac {\textit {\_f}}{4}-b \right ) {\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}\right ) \textit {\_g} \left (\textit {\_f} \right )}{{\mathrm e}^{\left (c_{1}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} \right ) \left (a -b \right )}-1}d \textit {\_f}}\right \}\right ]\right )\right \}\]