(Part 1:)
Use the symbols provided below to sketch the phase line for the differential equation
$$\dot{x} = 1+\frac{1}{2}\cos x.$$

To place a symbol on the line click a symbol button then click a point on the line.
To remove a symbol from the line click the "delete" button then click the symbol on the line.

(Part 2:)
What does your qualitative analysis tell you about the solutions of this differential equation?
Solutions are bounded and oscillate up and down.
Solutions are unbounded from below, and increase toward a finite upper bound as the independent variable approaches $\infty$.
The graphs of solutions spiral in loops that intersect each other when the independent variable increases by $2 \pi$.
Solutions are strictly increasing, and they tend toward $\pm \infty$ as the independent variable approaches $\pm \infty$.