Question

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

Answer 1

We have,
\[y = mx . . . . . \left( 1 \right) \]
Differentiating with respect to x
\[ \Rightarrow \frac{dy}{dx} = m\]
\[\text{ Substituting the value of m }= \frac{dy}{dx} \text{ in eq }\left( 1 \right)\text{ we get , }\]
\[y = x\frac{dy}{dx}\]
\[\text{ Hence, }y = x\frac{dy}{dx} \text{ is the required differential equation . }\]