\[ -f(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)-6 \sin ^6(x) y''(x)-4 \sin ^5(x) \cos (x) y'(x)+y(x) \sin ^6(x)=0 \] ✗ Mathematica : cpu = 0.0677754 (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 = 0.513 (sec), leaf count = 638
\[ \left \{ y \left ( x \right ) ={\frac {1}{48\, \left ( {{\rm e}^{2\,ix}}-1 \right ) ^{4}\sin \left ( x \right ) } \left ( 12\, \left ( {{\rm e}^{2\,ix}}-3/2\,{{\rm e}^{4\,ix}}+{{\rm e}^{6\,ix}}-1/4\,{{\rm e}^{8\,ix}}-1/4 \right ) \left ( {x}^{2}+{\frac {20}{3}} \right ) fx\ln \left ( 1-{{\rm e}^{ix}} \right ) -80\,i \left ( {{\rm e}^{2\,ix}}-{\frac {3\,{{\rm e}^{4\,ix}}}{2}}+{{\rm e}^{6\,ix}}-{\frac {{{\rm e}^{8\,ix}}}{4}}-{\frac {1}{4}} \right ) f{\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) +72\,i \left ( {{\rm e}^{2\,ix}}-{\frac {3\,{{\rm e}^{4\,ix}}}{2}}+{{\rm e}^{6\,ix}}-{\frac {{{\rm e}^{8\,ix}}}{4}}-{\frac {1}{4}} \right ) f{\it polylog} \left ( 4,{{\rm e}^{ix}} \right ) -12\, \left ( {{\rm e}^{2\,ix}}-3/2\,{{\rm e}^{4\,ix}}+{{\rm e}^{6\,ix}}-1/4\,{{\rm e}^{8\,ix}}-1/4 \right ) f{x}^{3}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) -12\, \left ( {{\rm e}^{2\,ix}}-3/2\,{{\rm e}^{4\,ix}}+{{\rm e}^{6\,ix}}-1/4\,{{\rm e}^{8\,ix}}-1/4 \right ) \left ( {x}^{2}+{\frac {20}{3}} \right ) fx\ln \left ( {{\rm e}^{ix}}+1 \right ) +80\,i \left ( {{\rm e}^{2\,ix}}-{\frac {3\,{{\rm e}^{4\,ix}}}{2}}+{{\rm e}^{6\,ix}}-{\frac {{{\rm e}^{8\,ix}}}{4}}-{\frac {1}{4}} \right ) f{\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) -72\,i \left ( {{\rm e}^{2\,ix}}-{\frac {3\,{{\rm e}^{4\,ix}}}{2}}+{{\rm e}^{6\,ix}}-{\frac {{{\rm e}^{8\,ix}}}{4}}-{\frac {1}{4}} \right ) f{\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) + \left ( 48\,{\it \_C4}\,{x}^{3}+48\,{\it \_C3}\,{x}^{2}+48\,{\it \_C2}\,x+48\,{\it \_C1} \right ) \left ( {{\rm e}^{2\,ix}} \right ) ^{4}+ \left ( -192\,{\it \_C4}\,{x}^{3}-192\,{\it \_C3}\,{x}^{2}-192\,{\it \_C2}\,x-192\,{\it \_C1} \right ) \left ( {{\rm e}^{2\,ix}} \right ) ^{3}+ \left ( 288\,{\it \_C4}\,{x}^{3}+288\,{\it \_C3}\,{x}^{2}+288\,{\it \_C2}\,x+288\,{\it \_C1} \right ) \left ( {{\rm e}^{2\,ix}} \right ) ^{2}+ \left ( 160\,{\it Artanh} \left ( {{\rm e}^{ix}} \right ) fx+8\,\csc \left ( x \right ) f{x}^{3} \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \cot \left ( x \right ) -192\,{\it \_C4}\,{x}^{3}-192\,{\it \_C3}\,{x}^{2}-192\,{\it \_C2}\,x-192\,{\it \_C1} \right ) {{\rm e}^{2\,ix}}-240\,f \left ( {\it Artanh} \left ( {{\rm e}^{ix}} \right ) +1/20\,\csc \left ( x \right ) \cot \left ( x \right ) {x}^{2} \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \right ) x{{\rm e}^{4\,ix}}+160\,f \left ( {\it Artanh} \left ( {{\rm e}^{ix}} \right ) +1/20\,\csc \left ( x \right ) \cot \left ( x \right ) {x}^{2} \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \right ) x{{\rm e}^{6\,ix}}-40\,f \left ( {\it Artanh} \left ( {{\rm e}^{ix}} \right ) +1/20\,\csc \left ( x \right ) \cot \left ( x \right ) {x}^{2} \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \right ) x{{\rm e}^{8\,ix}}-40\,{\it Artanh} \left ( {{\rm e}^{ix}} \right ) fx+12\,f \left ( {\frac {11\,{x}^{3}}{6}}+i \right ) {{\rm e}^{3\,ix}}-12\,f \left ( -{\frac {11\,{x}^{3}}{6}}+i \right ) {{\rm e}^{5\,ix}}+4\,f \left ( -3/2\,{x}^{3}+i \right ) {{\rm e}^{7\,ix}}-4\,f \left ( 3/2\,{x}^{3}+i \right ) {{\rm e}^{ix}}-2\,\csc \left ( x \right ) f{x}^{3} \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \cot \left ( x \right ) +48\,{\it \_C4}\,{x}^{3}+48\,{\it \_C3}\,{x}^{2}+48\,{\it \_C2}\,x+48\,{\it \_C1} \right ) } \right \} \]