The particular solution of the differential equation $\log \left(\frac{d y}{d x}\right)=x$, when $x=0, y=1$ is ..............

The solution of the differential equation $y d x-x d y=x y d x$ is ......

The solution of the differential equation $\frac{d \theta}{d t}=-k\left(\theta-\theta_0\right)$ where $k$ is constant, is .............

The order of the differential equation of all circles whose radius is 4 , is ...........