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

The rate of increase of the population of a city is proportional to the population present at that instant. In the period of 40 years the population increased from 30,000 to 40,000 . At any time t the population is $(a)(b)^{\frac{t}{40}}$. Then the values of $a$ and $b$ are respectively

The equation of the curve passing through origin and satisfying $\left(1+x^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=4 x^2$ is

The order of the differential equation whose general solution is given by $y=\left(\mathrm{C}_1+\mathrm{C}_2\right) \sin \left(x+\mathrm{C}_3\right)-\mathrm{C}_4 \mathrm{e}^{x+\mathrm{C}_5}$ is (where $\mathrm{C}_1, \mathrm{C}_2, \mathrm{C}_3, \mathrm{C}_4, \mathrm{C}_5$ are arbitrary constants)