ODE
\[ y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
Change of Variable, new dependent variable
Mathematica ✗
cpu = 23.7205 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x] == 1 - f[x]*Sin[y[x]] - Cos[y[x]]*(1 - Derivative[1][f][x]) + Derivative[1][f][x], y[x], x]
Maple ✓
cpu = 1.381 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) -2\,\arctan \left ( {\frac {-{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}xf \left ( x \right ) +{\it \_C1}\,f \left ( x \right ) }{{\it \_C1}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}} \right ) =0 \right \} \] Mathematica raw input
DSolve[y'[x] == 1 - f[x]*Sin[y[x]] - Cos[y[x]]*(1 - f'[x]) + f'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x] == 1 - f[x]*Sin[y[x]] - Cos[y[x]]*(1 - Derivative[1][f][x]) + Derivative[1][f][x], y[x], x]
Maple raw input
dsolve(diff(y(x),x) = 1+diff(f(x),x)-f(x)*sin(y(x))-(1-diff(f(x),x))*cos(y(x)), y(x),'implicit')
Maple raw output
y(x)-2*arctan((-exp(Int(f(x),x))+Int(exp(Int(f(x),x)),x)*f(x)+_C1*f(x))/(_C1+Int(exp(Int(f(x),x)),x))) = 0