\[ y'(x)=-y(x) \left (-\text {$\_$F1}(x)-\frac {\log (y(x))}{x}+\cot (x) \log (y(x))\right ) \] ✓ Mathematica : cpu = 3.5578 (sec), leaf count = 53
\[\text {Solve}\left [c_1+2 \sin (1) \log (y(x))=\int _1^x \frac {2 K[1] \sin (K[1]) \text {$\_$F1}(K[1])+2 \log (y(x)) (\sin (K[1])-K[1] \cos (K[1]))}{K[1]^2} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.681 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {x{\it \_C1}}{\sin \left ( x \right ) }}}}{{\rm e}^{{\frac {x}{\sin \left ( x \right ) }\int \!{\frac {{\it \_F1} \left ( x \right ) \sin \left ( x \right ) }{x}}\,{\rm d}x}}} \right \} \]