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

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

If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{dy}{dx} = \frac{2x-5y+3}{5x+2y-3}$,then the equation of that curve is:

If the slope of the tangent to a curve at any point $(x, y)$ is given by $3x^2 + 2x + 5$ and the curve passes through the point $(0, 1)$,then the equation of the curve is:

The population of a town increases at a rate proportional to the population at that time. If the population increases from $40,000$ to $80,000$ in $20$ years,then the population in another $40$ years will be (in $,000$)

$A$ population $P$ grows at the rate given by the equation $\frac{dP}{dt} = 0.05 P$. In how many years will the population double?