Let the population of rabbits surviving at time $t$ be governed by the differential equation $\frac{dp(t)}{dt} = \frac{1}{2}p(t) - 200$. If $p(0) = 100$,then $p(t)$ equals:

If $\frac{d^{2} y}{d x^{2}}=\sin x+e^{x}$,$y(0)=3$,and $\frac{d y}{d x}$ at $x=0$ is $4$,then find the equation of the curve.

The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ $10$ lakhs and due to loss they reduce to ₹ $10000$ after $3$ years,then the number of years required for the person to be bankrupt will be

$A$ population grows at the rate of $10 \%$ of the population per year. How long does it take for the population to double?

The microorganisms double themselves in $3$ hours. Assuming that the quantity increases at a rate proportional to itself,then the number of times it multiplies itself in $18$ hours is:

The solution of the differential equation $y \frac{dy}{dx} + x = k$ represents . . . . . . .