4.1.49 $y^{\prime }(x)=\cos (x)-y(x)(\sin (x)-y(x))$

ODE
$$y^{\prime }(x)=\cos (x)-y(x)(\sin (x)-y(x))$$ ODE Classification

[_Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica ✓
cpu = 6.56183 (sec), leaf count = 57

$$\left\{\{y(x)\to \frac{c_1\sin (x)({\int }_1^x{e}^{-\cos (K[1])}dK[1])+c_1(-e^{-\cos (x)})+\sin (x)}{c_1{\int }_1^x{e}^{-\cos (K[1])}dK[1]+1}\}\right\}$$

Maple ✓
cpu = 0.175 (sec), leaf count = 25

$$\{y\left(x\right)=-\frac{{\mathrm{e}}^{-\cos \left(x\right)}}{\mathit{\_}\mathit{C}\mathit{1}+\int {\mathrm{e}}^{-\cos \left(x\right)}\mathrm{d}x}+\sin \left(x\right)\}$$ Mathematica raw input

DSolve[y'[x] == Cos[x] - (Sin[x] - y[x])*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (-(C[1]/E^Cos[x]) + Sin[x] + C[1]*Integrate[E^(-Cos[K[1]]), {K[1], 1, 
x}]*Sin[x])/(1 + C[1]*Integrate[E^(-Cos[K[1]]), {K[1], 1, x}])}}

Maple raw input

dsolve(diff(y(x),x) = cos(x)-(sin(x)-y(x))*y(x), y(x),'implicit')

Maple raw output

y(x) = -1/(_C1+Int(exp(-cos(x)),x))*exp(-cos(x))+sin(x)