The differential equation of the family of straight lines y = mx is

Question

Question

This question was previously asked in

TNUSRB SI 2010 Official Paper (Held on 04 July 2010)

Answer 1

Explanation:

The differential equation of the family of straight lines

y = m x

$y = mx$ can be obtained by differentiating both sides with respect to

x

$x$ .

The derivative of

y

$y$ with respect to

x

$x$ is

d y / d x

$dy/dx$ , and the derivative of

m x

$mx$ with respect to

x

$x$ is

m

$m$ , because

m

$m$ is a constant. So, we have:

d y / d x = m

$dy/dx = m$

This is the differential equation representing the family of straight lines

y = m x

$y = mx$ . Therefore, the correct answer is option 1)

d y / d x = m

$dy/dx = m$ .