Brittany and I chose to go into detail about the third project of the semester. The topic of the project was to analyze the behavior of a system of two linked linear order differential equations. In the above equations a, b, c, and d are constants and. 1 Two distinct real roots.

We completed project one on newtons law of cooling and made a presentation of our work. Using the method of seperation of variables, this equation can be solved so that. Is the final temperature of the body,. Solving to determine the temperature of a Tea Cup,.

The first graph pictured below is the easiest of the graphs to obtain. Using the simple quadratic formula. The aim was to obtain two real roots greater than zero. The vector field plot seen below for this first case can be seen to be follow the source trend. The eigenvalues used to obtain this vector field plot are. Here is how this was done.

I am going to cut right to the point and explain some graphs we were able to produce in MatLab, rather then just ramble on with useless paragraphs of information. Here is the MatLab code that we used to provide the approximate curves for the graphs below.