Supposing to have a canonical ellipse (or other conics, parabola, circle, or hyperbola):
$$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \quad \text{or} \quad \frac{(x-x_0)^2}{a^{2}}+\frac{(y-y_0)^2}{b^{2}}=1$$
What is the meaning of the differentiating an ellipse for the ODE?
Related: Why do We differentiate doubly?
PS: I ask this question for students of an high school.