MAT 514 Project 1

Project Description

This project involves experimentation with the differential equation

y'=0.1*y+k*x

Here y is an unknown function of variable x, and k is a constant coefficient to be determined. One possible interpretation of this equation is that y(x) is the population size at time x. Natural growth is described by the term 0.1*y and migration by the term k*x.

Your goal

is to choose k so that the solution with initial condition
y(0) = 1st digit of your SUID
will hit the target
y(5) = 2nd digit of your SUID

This will involve some guessing along with observations on how the solution changes as you vary k (which may be positive or negative).

Technical Details

For this project I recommend using the applet Slope Field Calculator although you are free to use your favorite math software package instead. When you get y(5) to be reasonably close to the desired value, take the screenshot and submit it via Blackboard

About the applet

The equation should be entered as dy/dx = 0.1*y+0.23*x where instead of +0.23 you will have a different value of k.

The values Min x, Max x, Min y, Max y determine the viewing window.

The line "Add init.cond:" should have x = 0 and y = 1st digit of your SUID.

You do not have to change any other values.

The applet has two Submit buttons: one for equation and one for initial value. Press both.