\[ \boxed { \left ( x-a \right ) ^{5} \left ( x-b \right ) ^{5}{\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) -cy \left ( x \right ) =0} \]
Mathematica: cpu = 343.290592 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(a-\unicode {f817})^5 (b-\unicode {f817})^5 \unicode {f818}^{(5)}(\unicode {f817})-c \unicode {f818}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4,\unicode {f818}^{(4)}(0)=c_5\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 1.794 (sec), leaf count = 1258 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\frac { \left ( {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} } \right ) ^{2}{\it \_f}+4\, \left ( {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}} \right ) ^{2}b-2\,{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}}{\it \_f}-4\,a{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}}-4\,b{{\rm e}^{ \left ( \int \!{\it \_g} \left ( { \it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}+{\it \_f}+4\,a}{{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}} \left ( {a}^{2}-2\,ab+{b}^{2} \right ) } \left ( { \frac {b \left ( {\it \_g} \left ( {\it \_f} \right ) a-{\it \_g} \left ( {\it \_f} \right ) b \right ) {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1 } \right ) b}}}{{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} }-1}}-{\frac { \left ( b{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{ \it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}-a \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) a-{ \it \_g} \left ( {\it \_f} \right ) b \right ) {{\rm e}^{ \left ( \int \!{ \it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d} {\it \_f}+{\it \_C1} \right ) b}}}{ \left ( {{\rm e}^{ \left ( \int \!{ \it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d} {\it \_f}+{\it \_C1} \right ) b}}-1 \right ) ^{2}}} \right ) }\,{\rm d}{ \it \_f}+{\it \_C2}}},[ \left \{ \left ( -{{\it \_f}}^{5}-10\,{{\it \_f }}^{4}a-10\,{{\it \_f}}^{4}b-35\,{{\it \_f}}^{3}{a}^{2}-90\,{{\it \_f} }^{3}ab-35\,{{\it \_f}}^{3}{b}^{2}-50\,{{\it \_f}}^{2}{a}^{3}-270\,{{ \it \_f}}^{2}{a}^{2}b-270\,{{\it \_f}}^{2}a{b}^{2}-50\,{{\it \_f}}^{2} {b}^{3}-24\,{\it \_f}\,{a}^{4}-304\,{\it \_f}\,{a}^{3}b-624\,{\it \_f} \,{a}^{2}{b}^{2}-304\,{\it \_f}\,a{b}^{3}-24\,{\it \_f}\,{b}^{4}-96\,{ a}^{4}b-416\,{a}^{3}{b}^{2}-416\,{a}^{2}{b}^{3}-96\,a{b}^{4}+c \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{5}+ \left ( -10\,{{\it \_f}}^{3}-60\,{{\it \_f}}^{2}a-60\,{{\it \_f}}^{2}b -105\,{\it \_f}\,{a}^{2}-270\,{\it \_f}\,ab-105\,{\it \_f}\,{b}^{2}-50 \,{a}^{3}-270\,{a}^{2}b-270\,a{b}^{2}-50\,{b}^{3} \right ) \left ( { \it \_g} \left ( {\it \_f} \right ) \right ) ^{4}+ \left ( -15\,{\it \_f} -30\,a-30\,b \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{3}+ \left ( 10\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{ \it \_g} \left ( {\it \_f} \right ) \right ) {{\it \_f}}^{2}+40\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {\it \_f}\,a+40\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {\it \_f}\,b+35\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {a}^{2}+90\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}} }{\it \_g} \left ( {\it \_f} \right ) \right ) ab+35\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {b}^{2} \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{ 2}+ \left ( 5\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{{\it \_f}}^{2}}}{ \it \_g} \left ( {\it \_f} \right ) \right ) {\it \_f}+10\, \left ( { \frac {{\rm d}^{2}}{{\rm d}{{\it \_f}}^{2}}}{\it \_g} \left ( {\it \_f} \right ) \right ) a+10\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{{\it \_f} }^{2}}}{\it \_g} \left ( {\it \_f} \right ) \right ) b+10\,{\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {\it \_g} \left ( {\it \_f} \right ) -15\, \left ( {\frac {\rm d}{{\rm d} {\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{\it \_f}- 30\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f } \right ) \right ) ^{2}a-30\, \left ( {\frac {\rm d}{{\rm d}{\it \_f}}} {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}b+{\frac {{\rm d}^{3}} {{\rm d}{{\it \_f}}^{3}}}{\it \_g} \left ( {\it \_f} \right ) -10\,{ \frac { \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{{\it \_f}}^{2}}}{ \it \_g} \left ( {\it \_f} \right ) }{{\it \_g} \left ( {\it \_f} \right ) }}+15\,{\frac { \left ( {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) \right ) ^{3}}{ \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}}}=0 \right \} , \left \{ {\it \_f}={ \frac {{x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac {ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac {bx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}+{\frac {ab{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}-4\,x,{\it \_g} \left ( {\it \_f} \right ) =-{\frac {1}{a-b} \left ( \left ( x-b \right ) ^{-1}- \left ( x-a \right ) ^{-1} \right ) \left ( {x}^{2} \left ( {\frac {{ \frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}} \right ) -x \left ( {\frac {{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}} \right ) a-x \left ( {\frac {{\frac {{\rm d}^{2 }}{{\rm d}{x}^{2}}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}} \right ) b+ \left ( {\frac {{ \frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}} \right ) ab+2\,{\frac {x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ y \left ( x \right ) }}-{\frac {a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}-{\frac {b{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }}-4 \right ) ^{-1}} \right \} , \left \{ x={\frac {b{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f } \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} }-a}{{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}-1} },y \left ( x \right ) ={{\rm e}^{\int \!{\frac { \left ( {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}} \right ) ^{2}{\it \_f}+4\, \left ( {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}} \right ) ^{2}b-2\,{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} }{\it \_f}-4\,a{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} }-4\,b{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}+{ \it \_f}+4\,a}{{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b} } \left ( {a}^{2}-2\,ab+{b}^{2} \right ) } \left ( {\frac {b \left ( {\it \_g} \left ( {\it \_f} \right ) a-{\it \_g} \left ( {\it \_f} \right ) b \right ) {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}}{{ {\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{ \it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f } \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}-1}}-{\frac { \left ( b{{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) b}}-a \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) a-{\it \_g} \left ( {\it \_f} \right ) b \right ) {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}}}{ \left ( {{\rm e}^{ \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C1} \right ) a- \left ( \int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{ \it \_C1} \right ) b}}-1 \right ) ^{2}}} \right ) }\,{\rm d}{\it \_f}+{ \it \_C2}}} \right \} ] \right ) \right \} \]