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]
