4.3.12 \(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\)

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

\[ \left \{ y \relax (x ) -2\,\arctan \left ({\frac {-{{\rm e}^{\int \!f \relax (x ) \,{\rm d}x}}+\int \!{{\rm e}^{\int \!f \relax (x ) \,{\rm d}x}}\,{\rm d}xf \relax (x ) +{\it \_C1}\,f \relax (x ) }{{\it \_C1}+\int \!{{\rm e}^{\int \!f \relax (x ) \,{\rm d}x}}\,{\rm d}x}} \right ) =0 \right \} \] 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