The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$

The particular solution of the differential equation $$y(1+\log x) \frac{d x}{d y}-x \log x=0$$ when $$x=e, y=e^2$$ is

The order and degree of the differential equation $$\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$$ are respectively

The general solution of the differential equation $$\cos (x+y) \frac{d y}{d x}=1$$ is