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Question
Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.
Solution
We have,
y = mx .........(1)
Differentiating both sides, we get
\[\frac{dy}{dx} = m\]
\[ \Rightarrow \frac{dy}{dx} = \frac{y}{x} ............\left[\text{From (1)} \right]\]
\[ \Rightarrow x\frac{dy}{dx} = y\]
\[ \Rightarrow x\frac{dy}{dx} - y = 0\]
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