\[ y'(x)=-y(x) \left (-\text {$\_$F1}(x)-\frac {\log (y(x))}{x}+\cot (x) \log (y(x))\right ) \] ✓ Mathematica : cpu = 0.71596 (sec), leaf count = 106
\[\text {Solve}\left [\int _1^x\left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}-\frac {2 (\cos (K[1]) \log (y(x))-\sin (K[1]) \text {$\_$F1}(K[1]))}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 \sin (x)}{x K[2]}-\int _1^x\left (\frac {2 \sin (K[1])}{K[1]^2 K[2]}-\frac {2 \cos (K[1])}{K[1] K[2]}\right )dK[1]\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.2 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {{\it \_C1}\,x}{\sin \left ( x \right ) }}}}{{\rm e}^{{\frac {x}{\sin \left ( x \right ) }\int \!{\frac {{\it \_F1} \left ( x \right ) \sin \left ( x \right ) }{x}}\,{\rm d}x}}} \right \} \]