\[ y'(x)=y(x) \left (\text {$\_$F1}(x)+\frac {\log (y(x))}{x}-\cot (x) \log (y(x))\right ) \] ✓ Mathematica : cpu = 0.779976 (sec), leaf count = 106
DSolve[Derivative[1][y][x] == y[x]*(Log[y[x]]/x - Cot[x]*Log[y[x]] + _F1[x]),y[x],x]
\[\text {Solve}\left [\int _1^x\left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}-\frac {2 (\cos (K[1]) \log (y(x))-\sin (K[1]) \text {$\_$F1}(K[1]))}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 \sin (x)}{x K[2]}-\int _1^x\left (\frac {2 \sin (K[1])}{K[1]^2 K[2]}-\frac {2 \cos (K[1])}{K[1] K[2]}\right )dK[1]\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.02 (sec), leaf count = 30
dsolve(diff(y(x),x) = -(-1/x*ln(y(x))+1/sin(x)*cos(x)*ln(y(x))-_F1(x))*y(x),y(x))
\[y \left (x \right ) = {\mathrm e}^{\frac {x c_{1}}{\sin \left (x \right )}} {\mathrm e}^{\frac {x \left (\int \frac {\textit {\_F1} \left (x \right ) \sin \left (x \right )}{x}d x \right )}{\sin \left (x \right )}}\]