Problem $2.$ Consider the ODE and IC:

$x=2cost(x-\frac{x^2}{6})$

$x(0)=2$

a$)$ Determine the type of this ODE.

b$)$ Use the separation of variables method to calculate

the solution $x(t)$ analytically.

c$)$ Use Matlab to plot the analytical solution $x(t)$ over

the interval tin$[0,20].$

d$)$ Calculate the solution numerically in Matlab, plot

it$,$ and compare it to the analytical solution.

e$)$ Include your Matlab codes in your submission.