Question

The differential equation of the family of straight lines which passes through the origin is

• A. $y=x\frac{dy}{dx}$
• B. $y+x\frac{dy}{dx}=0$
• C. $x+y\frac{dy}{dx}=0$
• D. $\frac{dy}{dx}=m$

Answer 1

The correct option is A $y=x\frac{dy}{dx}$

Let us consider the problem:

Let us equation $y=mx$

When

m is the parameter

Passes through the origin

$y=mx$ (1)

Implies that

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

Differentiating equation (1) to $x$

$y=mx$

$\frac{dy}{dx}=m\times 1$

Implies that

$\frac{dy}{dx}=m$

Implies that

$\frac{dy}{dx}=\frac{y}{x}$

$y=x\frac{dy}{dx}$