Question

Differential equation representing the family of curves y is equals to mx where m is arbitrary constant is

Answer 1

Step-by-step explanation:

Given y=mx where m is an arbitrary constant. Differentiating both sides, we get dydx=m. Substituting for m=dydx in y=mx, we get: ⇒y=dydxx→xdydx−y=0.if you like this answer please mark me down as a brainliest

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Answer 2

ANSWER:-

We have

$\sf\red{y=mx.......(i)}$

Differentiating both sides of equation (i) with respect to x,we get

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

Substituting the value of m in equation (i),we get

$\sf\blue{y = \frac{dy}{dx} .x}$

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

which is free from the parameter m and hence this is the required differential equation.