\[ y'(x)=y(x) \left (\text {$\_$F1}(x)+\frac {\log (y(x))}{x}-\cot (x) \log (y(x))\right ) \] ✓ Mathematica : cpu = 0.931995 (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 = 0.796 (sec), leaf count = 30
\[\left \{y \left (x \right ) = {\mathrm e}^{\frac {c_{1} x}{\sin \left (x \right )}} {\mathrm e}^{\frac {x \left (\int \frac {\textit {\_F1} \left (x \right ) \sin \left (x \right )}{x}d x \right )}{\sin \left (x \right )}}\right \}\]