a project1 $18.pdf (page 3 of 4) Objectives: 1. Students will learn how to create an m- file in Matlab. 2. Students will use Matlab to solve first-order ODEs. 3. Students will understand the concepts of initial conditions and final values. Introduction The mathematical solution of many real- life problems involves exponential functions of the form: y()-e+c2e-r r where t is time and is the time constant. These solutions can altermatively be written in the form: y()-y()+(0)-yo)ewhere y(o) is the steady state solution. This form can give you added insight and can help you validate your solutions. It also enables you to model exponential problems from your data only. dy Given: +3y = 12 dt 1. Solve this differential equation by hand 2. Create an m- file with the following text in it and save it as odel.m to your personal space. Notice that your personal space may not be in the search path of MATLAB (eg. to set floppy drive to the search path, you should type: path(path,'a:'")) function odel % solving y' + a- 0 p(t)y- 0 between t-a and t-b where y(t-a)-c b- 2.5 c- 3: [T, Y]-ode23 (efirstorder, [a,bl.c) plot (T,Y) function dy firstorder (t,y) d- 12: 3. Type ode1 in the Matlab command window (a plot should appear) 4. Compare the plotted results with your solution by hand (or better yet plot your solution using MATLAB with part I procedure) 5 Change the initial condition c to a negative value, save the file and rerun 6. Use the original odel but increase the value of d and rerun. Tun in your hand-written or typed (with math editor) solutions plus a copy of the plots from steps 4 through 6. Comment on your observation of plots from these steps about objective 3 (in terms of initial and final values). Again, combine all plots and hand-written solutions into one file by Insert Picture in Microsoft Word