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.)

Question

asked Apr 17, 2021 8.5k views

1 Answer

Smk · Answer 1 · 2021-04-24T01:42:48+0000

Answer:

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

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