Patching and Plastering - vertical cracks along studs/window

In a bedroom I have two windows on different walls. Both have vertical cracks that run just about the full length of the wall. The cracks run below the window to the baseboard, then continue at the same spot above the window to the ceiling. The cracks are not located on the corners of the windows (which I hear is more common), but somwhere in the middle. One window has a single crack. The other window has 2 vertical cracks, both on studs (well not really sure what's behind there but my stud finder goes off at these spots).

A few years ago, I tried a simple compound and paint job. It lasted a few days maybe.

Next I tried a more thorough repair job, gouging out more of the drywall and used a mix of compound and some expandable type of filler (don't recall the name but it was recommended for this type of job). This repair lasted a little longer, but not much.

I would like to get a permanent repair; not sure if I can do it myself or if I should hire someone. How should I go about this? My next step was to use drywall tape along with compound. But I was thinking do I need to screw down the drywall? Suppose there is some movement; what happens if the drywall is screwed down tight? Something has to give right?

Building is about 10 years old.

I would assume that being a fairly new structure that you have drywall. Drywall tape and joint compound is the correct way to repair this. Spackling or j/c alone won't give a lasting repair. Paper tape will last longer than the "sticky' tape. If you use sticky tape you must use a setting compound like durabond for the repair to last. There may be a stud behind the crack under the window but even if there isn't - a tape repair should hold up as long as the wall isn't subjected to abuse

Those are drywall joints opening up because of movement in the wall from settling or racking from wind or poor foundation. Perhaps some crawl space or basement water problems last winter? Or not enoough shear plywood on that wall, or diagonal braces. Have you looked underneath the wall in question (at foundation) for underlying problems? When retaping, try a series of 6" pieces (at right angles)across the joint seam tape to help hold the drywall together from movement.
Be safe, Gary