\[ \left (1-f'(x)\right ) \cos (y(x))-f'(x)+f(x) \sin (y(x))+y'(x)-1=0 \] ✓ Mathematica : cpu = 0.0574641 (sec), leaf count = 72
\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (\frac {1}{c_1 \exp \left (\int _1^x-f(K[1])dK[1]\right )+\exp \left (\int _1^x-f(K[1])dK[1]\right ) \int _1^x-\exp \left (-\int _1^{K[2]}-f(K[1])dK[1]\right )dK[2]}+f(x)\right )\right \}\right \}\] ✓ Maple : cpu = 0.841 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) =2\,\arctan \left ( {\frac {-{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}xf \left ( x \right ) +f \left ( x \right ) {\it \_C1}}{{\it \_C1}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}} \right ) \right \} \]