The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000 . At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000 . The difference of populations of towns A and B at the end of 1994 was

The general solution of the differential equation $\frac{d y}{d x}=\cot x \cdot \cot y$ is

The equation of a curve passing through $(1,0)$ and having slope of tangent at any point $(x, y)$ of the curve as $\frac{y-1}{x^2+x}$ is

The differential equation which represents the family of curves $y=c_1 e^{c_2 x}$, where $c_1, c_2$ are arbitrary constants is