\[ -f(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)-6 \sin ^6(x) y''(x)-4 \sin ^5(x) \cos (x) y'(x)+y(x) \sin ^6(x)=0 \] ✓ Mathematica : cpu = 8.53073 (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 = 0.622 (sec), leaf count = 638
\[\left \{y \left (x \right ) = \frac {-2 \left (\csc ^{2}\left (x \right )+\frac {3}{2}\right ) f \,x^{3} \cot \left (x \right ) \csc \left (x \right )-12 \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f \,x^{3} \ln \left (-\cot \left (x \right )+\csc \left (x \right )\right )+48 c_{4} x^{3}+48 c_{3} x^{2}-40 f x \arctanh \left ({\mathrm e}^{i x}\right )-240 \left (\frac {\left (\csc ^{2}\left (x \right )+\frac {3}{2}\right ) x^{2} \cot \left (x \right ) \csc \left (x \right )}{20}+\arctanh \left ({\mathrm e}^{i x}\right )\right ) f x \,{\mathrm e}^{4 i x}+160 \left (\frac {\left (\csc ^{2}\left (x \right )+\frac {3}{2}\right ) x^{2} \cot \left (x \right ) \csc \left (x \right )}{20}+\arctanh \left ({\mathrm e}^{i x}\right )\right ) f x \,{\mathrm e}^{6 i x}-40 \left (\frac {\left (\csc ^{2}\left (x \right )+\frac {3}{2}\right ) x^{2} \cot \left (x \right ) \csc \left (x \right )}{20}+\arctanh \left ({\mathrm e}^{i x}\right )\right ) f x \,{\mathrm e}^{8 i x}+12 \left (x^{2}+\frac {20}{3}\right ) \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f x \ln \left (-{\mathrm e}^{i x}+1\right )-12 \left (x^{2}+\frac {20}{3}\right ) \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f x \ln \left ({\mathrm e}^{i x}+1\right )+48 c_{2} x +72 i \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f \polylog \left (4, {\mathrm e}^{i x}\right )+80 i \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f \polylog \left (2, -{\mathrm e}^{i x}\right )-72 i \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f \polylog \left (4, -{\mathrm e}^{i x}\right )-80 i \left ({\mathrm e}^{2 i x}-\frac {3 \,{\mathrm e}^{4 i x}}{2}+{\mathrm e}^{6 i x}-\frac {{\mathrm e}^{8 i x}}{4}-\frac {1}{4}\right ) f \polylog \left (2, {\mathrm e}^{i x}\right )-4 \left (\frac {3 x^{3}}{2}+i\right ) f \,{\mathrm e}^{i x}+12 \left (\frac {11 x^{3}}{6}+i\right ) f \,{\mathrm e}^{3 i x}-12 \left (-\frac {11 x^{3}}{6}+i\right ) f \,{\mathrm e}^{5 i x}+4 \left (-\frac {3 x^{3}}{2}+i\right ) f \,{\mathrm e}^{7 i x}+48 c_{1}+\left (8 \left (\csc ^{2}\left (x \right )+\frac {3}{2}\right ) f \,x^{3} \cot \left (x \right ) \csc \left (x \right )-192 c_{4} x^{3}-192 c_{3} x^{2}+160 f x \arctanh \left ({\mathrm e}^{i x}\right )-192 c_{2} x -192 c_{1}\right ) {\mathrm e}^{2 i x}+\left (288 c_{4} x^{3}+288 c_{3} x^{2}+288 c_{2} x +288 c_{1}\right ) {\mathrm e}^{4 i x}+\left (-192 c_{4} x^{3}-192 c_{3} x^{2}-192 c_{2} x -192 c_{1}\right ) {\mathrm e}^{6 i x}+\left (48 c_{4} x^{3}+48 c_{3} x^{2}+48 c_{2} x +48 c_{1}\right ) {\mathrm e}^{8 i x}}{48 \left ({\mathrm e}^{2 i x}-1\right )^{4} \sin \left (x \right )}\right \}\]