\[ y'(x)^2 \sin (y(x))+2 x y'(x) \cos ^3(y(x))-\sin (y(x)) \cos ^4(y(x))=0 \] ✓ Mathematica : cpu = 0.0748295 (sec), leaf count = 81
DSolve[-(Cos[y[x]]^4*Sin[y[x]]) + 2*x*Cos[y[x]]^3*Derivative[1][y][x] + Sin[y[x]]*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (2 \left (-\frac {c_1{}^{3/2}}{\sqrt {x+c_1}}-\frac {\sqrt {c_1} x}{\sqrt {x+c_1}}\right )\right )\right \},\left \{y(x)\to \tan ^{-1}\left (2 \left (\frac {c_1{}^{3/2}}{\sqrt {x+c_1}}+\frac {\sqrt {c_1} x}{\sqrt {x+c_1}}\right )\right )\right \}\right \}\] ✓ Maple : cpu = 2.298 (sec), leaf count = 1134
dsolve(diff(y(x),x)^2*sin(y(x))+2*x*diff(y(x),x)*cos(y(x))^3-sin(y(x))*cos(y(x))^4=0,y(x))
\[\left [x \left (\textit {\_T} \right ) = \frac {\left (\cos ^{4}\left (\frac {\arctan \left (\frac {c_{1}^{2} \textit {\_T}^{2}-2 c_{1} \textit {\_T} \left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}+\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}}, -\frac {9 \left (\frac {\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{3}+\left (c_{1} \textit {\_T} +\frac {\sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}}{9}\right ) \left (c_{1} \textit {\_T} -\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}\right )\right )}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}\right )}{2}\right )-\textit {\_T}^{2}\right ) \sin \left (\frac {\arctan \left (\frac {c_{1}^{2} \textit {\_T}^{2}-2 c_{1} \textit {\_T} \left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}+\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}}, -\frac {9 \left (\frac {\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{3}+\left (c_{1} \textit {\_T} +\frac {\sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}}{9}\right ) \left (c_{1} \textit {\_T} -\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}\right )\right )}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}\right )}{2}\right )}{2 \textit {\_T} \cos \left (\frac {\arctan \left (\frac {c_{1}^{2} \textit {\_T}^{2}-2 c_{1} \textit {\_T} \left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}+\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}}, -\frac {9 \left (\frac {\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{3}+\left (c_{1} \textit {\_T} +\frac {\sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}}{9}\right ) \left (c_{1} \textit {\_T} -\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}\right )\right )}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}\right )}{2}\right )^{3}}, y \left (\textit {\_T} \right ) = \frac {\arctan \left (\frac {c_{1}^{2} \textit {\_T}^{2}-2 c_{1} \textit {\_T} \left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}+\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}}, -\frac {9 \left (\frac {\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}{3}+\left (c_{1} \textit {\_T} +\frac {\sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}}{9}\right ) \left (c_{1} \textit {\_T} -\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {1}{3}}\right )\right )}{\left (c_{1}^{3} \textit {\_T}^{3}+54 c_{1} \textit {\_T} +6 \sqrt {3}\, \sqrt {c_{1}^{2} \textit {\_T}^{2} \left (c_{1}^{2} \textit {\_T}^{2}+27\right )}\right )^{\frac {2}{3}}}\right )}{2}\right ]\]