$(20$ points$)$

For the differential equation

$x^{}=-cos(x)$

where $-x2$

a$.$ Sketch the vector field on the real line. Then, find all fixed points & classify their stability.

b$.$ For the intial condition $x(0)=-\frac{}{4},$ describe the flow of the trajectory.

c$.$ For the intial conition $x(0)=\frac{}{4},$ describe the flow of the trajectory.

d$.$ For the initial condition $x(0)=\frac{}{2},$ describe the flow of the trajectory.

e$.$ For the initial condition $x(0)=\frac{5}{4},$ describe the flow of the trajectory.