question_answer

Find the differential equation of the family of all straight lines passing through the origin.

Answer:

Let the general equation of the family of alt straight lines passing through the origin is y = mx                                      ... (i) On differentiating both sides w.r.t. x, we get             \[\frac{dy}{dx}=m\] \[\Rightarrow \]   \[\frac{dy}{dx}=\frac{y}{x}\]                               [from Eq. (i)] \[\Rightarrow \]   \[x\frac{dy}{dx}=y\]