The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is......

The solution of differential equation $\left(x^2+1\right) \frac{d y}{d x}+\left(y^2+1\right)=0$ is $\ldots$

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