If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^{-x}+B \cos x$ as its general solution is

The general solution of the differential equation $\frac{d y}{d x}+\frac{\sin (2 x+y)}{\cos x}+2=0$ is

The general solution of the differential equation $(9 x-3 y+5) d y=(3 x-y+1) d x$ is

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 y^2+1}{2 y^3-4 x y+y}$ is