\[ \left (1-f'(x)\right ) \cos (y(x))-f'(x)+f(x) \sin (y(x))+y'(x)-1=0 \] ✓ Mathematica : cpu = 0.0668998 (sec), leaf count = 72
\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (f(x)+\frac {1}{\exp \left (\int _1^x-f(K[1])dK[1]\right ) \int _1^x-\exp \left (-\int _1^{K[2]}-f(K[1])dK[1]\right )dK[2]+c_1 \exp \left (\int _1^x-f(K[1])dK[1]\right )}\right )\right \}\right \}\] ✓ Maple : cpu = 1.389 (sec), leaf count = 41
\[y \relax (x ) = 2 \arctan \left (\frac {-{\mathrm e}^{\int f \relax (x )d x}+\left (\int {\mathrm e}^{\int f \relax (x )d x}d x \right ) f \relax (x )+f \relax (x ) c_{1}}{c_{1}+\int {\mathrm e}^{\int f \relax (x )d x}d x}\right )\]