If $y = e^{-mx}$ is a solution of the differential equation $\frac{d^2y}{dx^2} + 4 \frac{dy}{dx} + 3y = 0$, then the values of $m$ are

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? $(e^{0.5} = 1.648)$

$A$ spherical mothball has an initial radius of $3 \text{ cm}$. Due to evaporation, the radius of the ball reduces to $1 \text{ cm}$ in $4 \text{ months}$. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area?

The population $P=P(t)$ at time $t$ of a certain species follows the differential equation $\frac{dP}{dt}=0.5 P-450$. If $P(0)=850$,then the time at which the population becomes zero is

In a bank,the principal increases continuously at the rate of $5 \%$ per year. An amount of $Rs. 1000$ is deposited in this bank. How much will it be worth after $10$ years? (Given: $e^{0.5} = 1.648$)

Any curve passes through the point $(3, -4)$. If the slope of the tangent to the curve at any point $(x, y)$ is $\frac{2y}{x}$,then the equation of the curve is . . . . . . .