List of top Applied Mathematics Questions on Differential Equations asked in CBSE CLASS XII

Assertion (A): The differential equation representing the family of curves $y = mx$, $m$ being an arbitrary constant, is \[ x \dfrac{dy}{dx} - y = 0 \]
Reason (R): For a family of curves, the differential equation is obtained by differentiating the equation of family with respect to $x$ and then eliminating the arbitrary constant, if any.
The rate of change of population $P(t)$ with respect to time $(t)$, where $\alpha$, $\beta$ are the constant birth and death rates, respectively, is