\[ \boxed { \cos \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{4}-y \left ( x \right ) \sin \left ( x \right ) =0} \]
Mathematica: cpu = 0.041005 (sec), leaf count = 98 \[ \left \{\left \{y(x)\to \frac {1}{\sqrt [3]{c_1 \cos ^3(x)-\sin (x)-2 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{c_1 \cos ^3(x)-\sin (x)-2 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{c_1 \cos ^3(x)-\sin (x)-2 \sin (x) \cos ^2(x)}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 364 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}},y \left ( x \right ) =-{ \frac {1}{2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+4 \,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-4 \,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-6\,\cos \left ( x \right ) \sin \left ( x \right ) +2\,{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{ 2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}}-{\frac {{\frac {i}{2}}\sqrt {3}}{{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}},y \left ( x \right ) =-{ \frac {1}{2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+4 \,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-4 \,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-6\,\cos \left ( x \right ) \sin \left ( x \right ) +2\,{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{ 2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}}+{\frac {{\frac {i}{2}}\sqrt {3}}{{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}} \right \} \]