\[ \left (1-f'(x)\right ) \cos (y(x))-f'(x)+f(x) \sin (y(x))+y'(x)-1=0 \] ✓ Mathematica : cpu = 0.0737126 (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 = 1.2 (sec), leaf count = 41
\[\left \{y \left (x \right ) = 2 \arctan \left (\frac {c_{1} f \left (x \right )+f \left (x \right ) \left (\int {\mathrm e}^{\int f \left (x \right )d x}d x \right )-{\mathrm e}^{\int f \left (x \right )d x}}{c_{1}+\int {\mathrm e}^{\int f \left (x \right )d x}d x}\right )\right \}\]