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

`(dy)/(dx)\ = ky_2`

Explanation:

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

`(dy)/(dx)`

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

`(dy)/(dx)\ \alpha \ y_2`

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

`(dy)/(dx)\ = ky_2`

where k is the constant of proportionality.

Hence the differential equation for the statement is expressed as
`(dy)/(dx)\ = ky_2`