\[ \boxed { {\it d4y} \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{6}+4\, \left ( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) \right ) \left ( \sin \left ( x \right ) \right ) ^{5}\cos \left ( x \right ) -6\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) \left ( \sin \left ( x \right ) \right ) ^{6}-4\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \left ( \sin \left ( x \right ) \right ) ^{5}\cos \left ( x \right ) +y \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{6}-f=0} \]
Mathematica: cpu = 0.067008 (sec), leaf count = 61 \[ \text {DSolve}\left [-f(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)-6 \sin ^6(x) y''(x)-4 \sin ^5(x) \cos (x) y'(x)+y(x) \sin ^6(x)=0,y(x),x\right ] \]
Maple: cpu = 0.265 (sec), leaf count = 1277 \[ \left \{ y \left ( x \right ) =-{\frac {f \left ( -12\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{{\rm e}^{6\,ix}}{ x}^{3}+80\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{ {\rm e}^{ix}} \right ) {{\rm e}^{6\,ix}}x-80\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{6 \,ix}}x+18\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{{\rm e}^{4\,ix}}{x}^{3}-12\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{6 \,ix}}{x}^{3}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^ {6\,ix}}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) {x}^{3}+3\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{{\rm e}^{8\,ix}}{x}^{3}-20\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{{\rm e}^{ix}} \right ) { {\rm e}^{8\,ix}}x-18\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{{\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}{x}^{3}+20\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}x+18\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}{x} ^{3}-18\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}} \ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) {x}^ {3}-3\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{ {\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}{x}^{3}+3\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{ 8\,ix}}{x}^{3}-3\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^ {8\,ix}}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) {x}^{3}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{{\rm e}^{ix}} \right ) {{\rm e}^{6\,ix}}{x}^{3}+2\,{x}^{3} \cos \left ( x \right ) +2\,\cos \left ( x \right ) {{\rm e}^{8\,ix}}{x}^{ 3}-120\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{ {\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}x+120\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{4 \,ix}}x+18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}+20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}-18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) {{\rm e}^{ 8\,ix}}-20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}-72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) {{\rm e}^{6\,ix}}-80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) {{\rm e}^{ 6\,ix}}+72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) {{\rm e}^{6\,ix}}+80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) {{\rm e}^{6\,ix}}+108\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) {{\rm e}^{4 \,ix}}+120\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}-108\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}-120\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) {{\rm e}^{4 \,ix}}-3\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{ {\rm e}^{ix}} \right ) {x}^{3}+3\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {x}^{3}+6\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{7\,ix}}{x}^{3}-22\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{5\,ix}}{x}^{3}+6 \, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{ix}}{x}^{3}-22 \, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{3\,ix}}{x}^{3}- 3\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) {x}^{3}+3\,{x}^{3}\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}-20\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{{\rm e}^{ix} } \right ) x+20\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) x-8\,\cos \left ( x \right ) {{\rm e}^{ 2\,ix}}{x}^{3}+18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) +20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) - 18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4 ,-{{\rm e}^{ix}} \right ) -20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) -4\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{7\,ix}}+12\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{5\,ix}}+4\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{ix}}-12\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{3\,ix}}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1+{{\rm e}^{ix}} \right ) { {\rm e}^{2\,ix}}{x}^{3}-12\, \left ( \sin \left ( x \right ) \right ) ^{4 }\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{2\,ix}}{x}^{3}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) {x}^{3}- 12\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{ {\rm e}^{2\,ix}}{x}^{3}+80\, \left ( \sin \left ( x \right ) \right ) ^{4 }\ln \left ( 1+{{\rm e}^{ix}} \right ) {{\rm e}^{2\,ix}}x-80\, \left ( \sin \left ( x \right ) \right ) ^{4}\ln \left ( 1-{{\rm e}^{ix}} \right ) {{\rm e}^{2\,ix}}x-72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) {{\rm e}^{2 \,ix}}-80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) {{\rm e}^{2\,ix}}+72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) {{\rm e}^{2\,ix}}+80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) {{\rm e}^{2 \,ix}}-8\,\cos \left ( x \right ) {{\rm e}^{6\,ix}}{x}^{3}+12\,\cos \left ( x \right ) {{\rm e}^{4\,ix}}{x}^{3}-160\, \left ( \sin \left ( x \right ) \right ) ^{4}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) { {\rm e}^{6\,ix}}x+240\, \left ( \sin \left ( x \right ) \right ) ^{4}{ \it Artanh} \left ( {{\rm e}^{ix}} \right ) {{\rm e}^{4\,ix}}x+40\, \left ( \sin \left ( x \right ) \right ) ^{4}{\it Artanh} \left ( { {\rm e}^{ix}} \right ) {{\rm e}^{8\,ix}}x-160\, \left ( \sin \left ( x \right ) \right ) ^{4}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) { {\rm e}^{2\,ix}}x+40\, \left ( \sin \left ( x \right ) \right ) ^{4}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x \right ) }{48\, \left ( {{\rm e} ^{2\,ix}}-1 \right ) ^{4} \left ( \sin \left ( x \right ) \right ) ^{5}}}+ {\frac {{\it \_C1}}{\sin \left ( x \right ) }}+{\frac {{\it \_C2}\,x}{ \sin \left ( x \right ) }}+{\frac {{\it \_C3}\,{x}^{2}}{\sin \left ( x \right ) }}+{\frac {{\it \_C4}\,{x}^{3}}{\sin \left ( x \right ) }} \right \} \]