##### 4.15.42 $$y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0$$

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

[NONE]

Book solution method
Exact equation

Mathematica
cpu = 122.898 (sec), leaf count = 0 , could not solve

DSolve[Cos[x] + Cos[x + y[x]] + Sin[x*y[x]]*y[x] + (Cos[x + y[x]] - Sin[y[x]] + a*Sin[x*y[x]])*Derivative[1][y][x] == 0, y[x], x]

Maple
cpu = 457.472 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

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

Mathematica raw output

DSolve[Cos[x] + Cos[x + y[x]] + Sin[x*y[x]]*y[x] + (Cos[x + y[x]] - Sin[y[x]] +
a*Sin[x*y[x]])*Derivative[1][y][x] == 0, y[x], x]

Maple raw input

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

Maple raw output

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