Question

The rate of change of y with respect to x is proportional to y2. Write a differential equation for the statement. (Use k for the constant of proportionality.)

Answer 1

Answer:

$\dfrac{dy}{dx}\ = ky_2$

Step-by-step explanation:

The rate of change of y with respect to x is expressed as shown;

$\dfrac{dy}{dx}$

If the rate of change of y with respect to x is proportional to y2, this is expressed as;

$\dfrac{dy}{dx}\ \alpha \ y_2$

If we remove the proportionality sign, a proportionality constant will be introduced as shown;

$\dfrac{dy}{dx}\ = ky_2$

where k is the constant of proportionality.

Hence the differential equation for the statement is expressed as $\dfrac{dy}{dx}\ = ky_2$