\[ -f(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)-6 \sin ^6(x) y''(x)-4 \sin ^5(x) \cos (x) y'(x)+y(x) \sin ^6(x)=0 \] ✗ Mathematica : cpu = 0.0654131 (sec), leaf count = 0 , could not solve
DSolve[-f[x] + Sin[x]^6*y[x] - 4*Cos[x]*Sin[x]^5*Derivative[1][y][x] - 6*Sin[x]^6*Derivative[2][y][x] + 4*Cos[x]*Sin[x]^5*Derivative[3][y][x] + Sin[x]^6*Derivative[4][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.399 (sec), leaf count = 1277
\[ \left \{ y \left ( x \right ) =-{\frac {f \left ( 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\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) {x}^{3}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \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}{{\rm e}^{2\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) x+80\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) x-160\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x+2\,{x}^{3}\cos \left ( x \right ) -108\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) +72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) -120\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) +108\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) +120\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) +80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) -72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) -80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) +20\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) x+18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) +20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) -18\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}{\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 ) +6\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{ix}}{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}-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\, \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 ( {{\rm e}^{ix}}+1 \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 ( {{\rm e}^{ix}}+1 \right ) x-8\,\cos \left ( x \right ) {{\rm e}^{2\,ix}}{x}^{3}+4\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{ix}}-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}}-12\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{3\,ix}}-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 ) +40\, \left ( \sin \left ( x \right ) \right ) ^{4}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x-8\,\cos \left ( x \right ) {{\rm e}^{6\,ix}}{x}^{3}+12\,\cos \left ( x \right ) {{\rm e}^{4\,ix}}{x}^{3}+2\,\cos \left ( x \right ) {{\rm e}^{8\,ix}}{x}^{3}+80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) -72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) -80\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) +72\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{2\,ix}}{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) +40\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x-160\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x+240\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}{\it Artanh} \left ( {{\rm e}^{ix}} \right ) x-20\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) x-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}+18\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) {x}^{3}-18\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) {x}^{3}-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}{{\rm e}^{6\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) x-120\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) x-20\,i \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) -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}+3\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) {x}^{3}-3\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{8\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) {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}+80\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) x+18\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{{\rm e}^{4\,ix}}{x}^{3}+120\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{4\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) x-12\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}\ln \left ( 1-{{\rm e}^{ix}} \right ) {x}^{3}+12\, \left ( \sin \left ( x \right ) \right ) ^{4}{{\rm e}^{6\,ix}}\ln \left ( {{\rm e}^{ix}}+1 \right ) {x}^{3}+3\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{2}{{\rm e}^{8\,ix}}{x}^{3} \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 \} \]