Length of a spring with mass m, length l, and spring constant k when suspended

[FrozenWinters]

A spring of mass m, length l, and spring constant of k, is suspended. What is its length at equilibrium?

My current approach: look at the change in expansion relative to distance of the unexpanded spring. However, the differential equation I revive is unsolvable.

 

[Matterwave]

F=-kx+mg...when does that equal 0? (This x gives the stretching)

 

[AlephZero]

My current approach: look at the change in expansion relative to distance of the unexpanded spring. However, the differential equation I revive is unsolvable.

That''s the right way to do it. See https://www.physicsforums.com/showthread.php?t=177689