prepared by Mark E. Johnson, maejohns@math.princeton.edu

# MATLAB Practice Problems

All problems on this page are taken directly from the textbook for the course : the 6th edition of Boyce and diPrima. This will give you a chance to reproduce some of the pictures they use in the text by using Matlab.

### Problem 1

On Page 20, in Example 2, you should find the differential equation
```y'-y/2=exp(-t)
```
Using Matlab, first reproduce the trajectories from Figure 2.1.3 on page 21 represeting the solution with initial condition y(0)=-1.

Then try to reproduce the entire picture by choosing several other initial conditions and integrating, all the while plotting solutions on the same y vs. t graph. (How do you print solutions on the same graph? Take a look at the hold command by typing help hold) Try labelling your axes and maybe rescaling them so they are nice and pretty. help axis, help title, help xlabel, etc. oughta do the trick...

Now print your solution. (you don't have to, but you should know how)

### Problem 2

On page 371, in Example 1 we have a linear system of equations which can be rewritten as
```x' = x + y
y' = 4x + y
```
Use Matlab to integrate this system and reproduce some of the trajectories in Figure 7.5.2. Note that the left plot is a phase portrait (y vs. x) and the right portrait is a plot of x vs. t. (My notations differs from that used in the text).

Again make sure you can plot multiple solutions on the same graph and make sure you know how to print.

### Problem 3

Page 505, Example 1 gives a systems of equations
```x' = x ( 1-.5 y )
y' = y ( -.75 + .25 x)
```
Try to (roughly) reproduce Figure 9.5.2 on page 507.