Computer not detecting Hard Drive

Lately my external Hard Drive has not been detected by my computer at all. I have tried it in all my computers USB ports, and it still doesn't show up in my computer or disk management, however other computers will recognize it immediately after it has been plugged in. Other Memory devices have been plugged in via USB port and it picks them up just fine.What can I do to fix it?
 
Back up the external drives files and format it on another computer, then try it again on the suspect computer
 
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