Code in MATLAB. Consider the following ODE:

$\frac{dx}{dt}=e^x-cos(x)$

Complete the following tasks:

a$.$ Plot $\frac{dx}{dt}$ vs$.$ x over a range of x values from $-6$ to $2.$

b$.$ Annotate this plot $($by hand$)$ to complete a phase portrait, i$.$e$.$ identify the fixed points and classify their stability.

c$.$ Sketch $($by hand$)$ the anticipated solution, $x(t),$ for an initial value of $x=-2.$

d$.$ Solve this ODE using MATLAB's ode$45()$ function for an initial value of $x=-2$ and a range of time $(t)$ values from $0$ to $10.$

e$.$ On a new figure, plot your solution, $x$ vs $t.$

f$.$ Briefly describe how your answers to Parts $($c$)$ and $($d$)$ compare.