DSolve[Derivative[1][y][x] == (x/2 + x^3/2 + x^4/2 + (x*Cos[2*y[x]])/2 + (x^3*Cos[2*y[x]])/2 + (x^4*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x]