The differential equation whose solution represents the family $x^2 y=4 \mathrm{e}^x+\mathrm{c}$, where c is an arbitrary constant, is

The differential equation of all straight lines passing through the point $(1,-1)$ is

The principal increases continuously in a newly opened bank at the rate of $10 \%$ per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years?

$$ \left(\mathrm{e}^{0.5}=1.648\right) $$

The solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=(x+y)^2$ is