# Form the Differential Equation Representing the Family of Curves Y = Mx, Where M is an Arbitrary Constant. - Mathematics

Sum

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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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 4 | Page 145