The integrating factor of the differential equation $(1 + t^2) + \left(x - e^{\tan^{-1}t}\right)\dfrac{dt}{dx} = 0$ is

The degree of the differential equation obtained from the equation $(y - a)^2 = 4(x - b)$ [where $a$ and b are arbitrary constants] is

The solution of the differential equation $\left(x + 2y^3\right)\dfrac{dy}{dx} - y = 0$ is

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in