The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in $3$ hours,then the number of times the bacteria are increased in $6$ hours is

The differential equation of displacement of all $Simple \ Harmonic \ Motions$ of given period $T = 2\pi / n$ is:

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 solution of $\frac{dy}{dx} = \frac{ax + b}{cy + d}$ represents a parabola if

The population of a city increases at the rate of $3 \%$ per year. If the population is $p$ at time $t$,then the equation of $p$ in terms of $t$ is . . . . . . .