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We study the stability of vortex-lines in trapped dilute gases subject to rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a 3d condensate in spherically and cilyndrically symmetric stationary traps, from small to very large nonlinearities. In the stationary case it is found that the vortex states with unit and m=2 charge are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the m=1doi:10.1103/physreva.60.4864 fatcat:s4cpcspad5botehlhgmrmcy5ii