\[ -f(x)-4 \sin ^5(x) \cos (x) y'(x)-6 \sin ^6(x) y''(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)+y(x) \sin ^6(x)=0 \] ✓ Mathematica : cpu = 7.17629 (sec), leaf count = 138
\[\left \{\left \{y(x)\to x^3 \csc (x) \int _1^x\frac {1}{6} \csc ^5(K[4]) f(K[4])dK[4]+x^2 \csc (x) \int _1^x-\frac {1}{2} \csc ^5(K[3]) f(K[3]) K[3]dK[3]+x \csc (x) \int _1^x\frac {1}{2} \csc ^5(K[2]) f(K[2]) K[2]^2dK[2]+\csc (x) \int _1^x-\frac {1}{6} \csc ^5(K[1]) f(K[1]) K[1]^3dK[1]+c_4 x^3 \csc (x)+c_3 x^2 \csc (x)+c_2 x \csc (x)+c_1 \csc (x)\right \}\right \}\] ✓ Maple : cpu = 0.767 (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\,f \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 ) x\ln \left ( 1-{{\rm e}^{ix}} \right ) +80\,if \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 ) {\it polylog} \left ( 2,-{{\rm e}^{ix}} \right ) -72\,if \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 ) {\it polylog} \left ( 4,-{{\rm e}^{ix}} \right ) -12\,f \left ( {{\rm e}^{2\,ix}}-3/2\,{{\rm e}^{4\,ix}}+{{\rm e}^{6\,ix}}-1/4\,{{\rm e}^{8\,ix}}-1/4 \right ) {x}^{3}\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) -12\,f \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 ) x\ln \left ( 1+{{\rm e}^{ix}} \right ) -80\,if \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 ) {\it polylog} \left ( 2,{{\rm e}^{ix}} \right ) +72\,if \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 ) {\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\,f \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) {x}^{3}\csc \left ( x \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\, \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \cot \left ( x \right ) {x}^{2}\csc \left ( x \right ) \right ) x{{\rm e}^{4\,ix}}+160\,f \left ( {\it Artanh} \left ( {{\rm e}^{ix}} \right ) +1/20\, \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \cot \left ( x \right ) {x}^{2}\csc \left ( x \right ) \right ) x{{\rm e}^{6\,ix}}-40\,f \left ( {\it Artanh} \left ( {{\rm e}^{ix}} \right ) +1/20\, \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) \cot \left ( x \right ) {x}^{2}\csc \left ( x \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\,f \left ( \left ( \csc \left ( x \right ) \right ) ^{2}+3/2 \right ) {x}^{3}\csc \left ( x \right ) \cot \left ( x \right ) +48\,{\it \_C4}\,{x}^{3}+48\,{\it \_C3}\,{x}^{2}+48\,{\it \_C2}\,x+48\,{\it \_C1} \right ) } \right \} \]