# 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.)

1 answer

###### 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.)

## Answers

Answer:[tex]\dfrac{dy}{dx}\ = ky_2[/tex]Step-by-step explanation:The rate of change of y with respect to x is expressed as shown;[tex]\dfrac{dy}{dx}[/tex]If the rate of change of y with respect to x is proportional to y2, this is expressed as;[tex]\dfrac{dy}{dx}\ \alpha \ y_2[/tex]If we remove the proportionality sign, a proportionality constant will be introduced as shown;[tex]\dfrac{dy}{dx}\ = ky_2[/tex]where k is the constant of proportionality.Hence the differential equation for the statement is expressed as [tex]\dfrac{dy}{dx}\ = ky_2[/tex]

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