Question

The differential equation of all straight lines passing through the origin is

• A. $y = \sqrt { x \frac { d y } { d x } }$
• B. $\frac { d y } { d x } = y + x$
• C. $\frac { d y } { d x } = \frac { y } { x }$
• D. None of these

Answer 1

Answer: (C)

$\frac { d y } { d x } = \frac { y } { x }$

Answer 2

The equation of all straight lines passing through the origin is $y = m x$ .….(i)

Where m is arbitrary constant

Differentiate (i) w.r.t. x, we get

$\frac { d y } { d x } = m$ ⇒ $\frac { d y } { d x } = \frac { y } { x }$ , (By (i)).