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