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I have two RES and they were both very tiny when I got them. They both began acting normal in the tank that I put them in (which, from what I know, has everything needed: water, basking area, heat lamp, filteration, etc.). One of them eats a lot and is very active and eats everything in site, begs for food, swims, and has grown substantially. But the other seems to get more and more lethargic and doesn't even seem to be eating. All it does is bask and barely even gets in the water. And recently it has started to cough and make strange gestures like it can't breathe or something. I would suspect that maybe the settings of the tank are off but the other turtle seems to thrive, so I'm not sure what is going on and I feel bad for the little guy.

First, seperate your turtles. Second, take him to a vet. It sounds like it has a Respiratory infection.

It also sounds like you need a UVB light.

Make sure that your water temperature is around 79-81 for the sick turtle, and around 75 for your other.

While you're looking for a qualified vet, separate the sick one and keep him warmer than usual (water temp 82F, basking area 90-91F). The added warmth will help him fight any infection. Keep him out of any drafts or breezes. Keep trying to get him to eat, try something smelly to whet his appetite.

The sooner you have him treated, the better chance he has for a smooth recovery.

what is something good to feed the sick one?

Smelly---bits of tuna or sardine are common "lures." You could also try some hardboiled egg white, cooked fish. Are his eyes open? If he can't see, try holding a little of the food in front of his nose in the water and see if he'll take it.

It would be good to have him looked at ASAP.

Where do you live? Do you already have a herp vet? It sounds like an RI, which won't get better on it's own, it needs vet treatment and anti-biotics.