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 = 191.247 (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 = 89.007 (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),'implicit')
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),'implicit')
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),'implicit')