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

- The autonomous equation

$\frac{dx}{dt}=x-2 \sin{x}.$ - The autonomous equation

$\frac{dx}{dt}=x-\frac{1}{2} \sin{x}.$ - 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:

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

See assignment here.

Download the MATLAB source by typing

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

at the MATLAB **>>** prompt.