Question

Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

Answer 1

We have,

y = mx          .........(1)

Differentiating both sides, we get

\[\frac{dy}{dx} = m\]
\[ \Rightarrow \frac{dy}{dx} = \frac{y}{x} ............\left[\text{From (1)} \right]\]
\[ \Rightarrow x\frac{dy}{dx} = y\]
\[ \Rightarrow x\frac{dy}{dx} - y = 0\]