##### 4.15.40 $$y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0$$

ODE
$y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0$ ODE Classiﬁcation

[NONE]

Book solution method
Exact equation

Mathematica
cpu = 0.792547 (sec), leaf count = 32

$\text {Solve}[2 y(x)+\sin (2 y(x))+2 x+\sin (2 x)+c_1=4 \sin (A) \sin (x) \sin (y(x)),y(x)]$

Maple
cpu = 0.616 (sec), leaf count = 35

$\left [\frac {\cos \left (x \right ) \sin \left (x \right )}{2}+\frac {x}{2}-\sin \left (y \left (x \right )\right ) \sin \left (A \right ) \sin \left (x \right )+\frac {\sin \left (y \left (x \right )\right ) \cos \left (y \left (x \right )\right )}{2}+\frac {y \left (x \right )}{2}+\textit {\_C1} = 0\right ]$ Mathematica raw input

DSolve[Cos[x]*(Cos[x] - Sin[A]*Sin[y[x]]) + Cos[y[x]]*(Cos[y[x]] - Sin[A]*Sin[x])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[2*x + C[1] + Sin[2*x] + Sin[2*y[x]] + 2*y[x] == 4*Sin[A]*Sin[x]*Sin[y[x]],
 y[x]]

Maple raw input

dsolve(diff(y(x),x)*cos(y(x))*(cos(y(x))-sin(A)*sin(x))+cos(x)*(cos(x)-sin(A)*sin(y(x))) = 0, y(x))

Maple raw output

[1/2*cos(x)*sin(x)+1/2*x-sin(y(x))*sin(A)*sin(x)+1/2*sin(y(x))*cos(y(x))+1/2*y(x
)+_C1 = 0]