The general solution of differential equation $\left(y^2-x^2\right) \mathrm{d} x=x y \mathrm{~d} y(x \neq 0)$ is

The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be

The differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 y$ represents ________

The solution of the equation $x^2 y-x^3 \frac{\mathrm{~d} y}{\mathrm{~d} x}=y^4 \cos x$, where $y(0)=1$, is