\[ y'(x)=-y(x) \left (-\text {$\_$F1}(x)-\frac {\log (y(x))}{x}+\cot (x) \log (y(x))\right ) \] ✓ Mathematica : cpu = 3.66868 (sec), leaf count = 56
\[\text {Solve}\left [\int _1^x \left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}-\frac {2 (\log (y(x)) \cos (K[1])-\sin (K[1]) \text {$\_$F1}(K[1]))}{K[1]}\right ) \, dK[1]-2 \sin (1) \log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.556 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {{\it \_C1}\,x}{\sin \left ( x \right ) }}}}{{\rm e}^{{\frac {x}{\sin \left ( x \right ) }\int \!{\frac {{\it \_F1} \left ( x \right ) \sin \left ( x \right ) }{x}}\,{\rm d}x}}} \right \} \]