# Matlab assignment 1

## Due week of February 19

### Part A

Using the program pplane1, plot the direction field and several solutions to the ordinary differential equations

1. The autonomous equation
$\frac{dx}{dt}=x-2 \sin{x}.$
2. The autonomous equation
$\frac{dx}{dt}=x-\frac{1}{2} \sin{x}.$
3. The non-autonomous equation
$\frac{dx}{dt}=t^2 x-x^3.$

It is up to you to pick the range over which you plot in $x$ and $t$ in order to see the behavior.

Print your answers to graphics files (From the ''File$\to$save as'' menu in the figure window, no screenshots!). And hand them in on paper along with your answer to the following questions:

1. What are all the equilibria of equation 1?
2. Which of these are stable and which are unstable?
3. Why do the results look so different in equations 1 and 2? Support your answer with math and graphs.
4. Describe the long-term behavior of equation 3 in words.

### Part B

See assignment here.

grabcode https://web.njit.edu/~goodman/Math222/matlab1A.html