Question

Differential equation of family of lines passing through origin

Answer 1

Let y=mx be the family of lines through origin. Therefore dy/dx = m. Eliminating m we get y=dy/dx . x or x dy/dx -y=0

Answer 2

Answer:

$\frac{dy}{dx} - \frac{y}{x} = 0$

Step-by-step explanation:

We know that to find the differential equation of family of curves,we have to find the equation of curve first.

Equation of line passing through origin

$y = mx \: \: \: \: \: eq1$

Now, differentiate the equation

$\frac{dy}{dx} = m \frac{dx}{dx} + x \frac{dm}{dx} \\ \\ \frac{dy}{dx} = m(1) + x(0) \\ \\ \frac{dy}{dx} = m \\ \\ now \: put \: the \: value \: of \: m \: from \: eq \: 1 \\ \\ \frac{dy}{dx} = \frac{y}{x} \\ \\ \frac{dy}{dx} - \frac{y}{x} = 0$

is the differential equation of family of lines passing through origin.

Hope you understand.