I rarely get flats when ride so I didn't notice that I got one until I arrived to my destination and it was a slow leak.
I replaced the tube that only been on my bike for two weeks.
When I got home I discovered that the schrader valve on my tube is leaking air.

Is this common for schrader valve tubes to have leaky valve?

Could it be posible that I did something wrong when aired up the tire or perhaps the tube is defected?

The valve should not leak. Probably the tube is defective or something got inside the valve and jammed it open slightly.

Leaky valves do happen. That's why they stock bags of valve cores at any auto parts store....

No rare as a honest con-man, but the cores are replaceable & cheap.

you tested it and found it leaking inside the stem?

I filled up a bathtub with a water and then I put the tube in the water to see where the tube would make bubbles.
The tube only bubbled around the valve and I could also hear air escaping from the valve.
The tube does not go 100% flat it still holds tiny bit of air.

And it's worth keeping a cap on them. It only takes a tiny bit of sand or debris to result in a leak next time you pump.

Valve cores can become damaged or loose. Valve stems can have their seats become damaged. Valve stems can become in bonded to their "rubber" jacket. Andy.

Valve cores are cheap, just replace it. I've had them fail due to trash so keep a valve cap on them. Also due to oil contamination causing the rubber or plastic on the valve to swell and stick. Many years ago there was a brand of imported tube that had zinc stems instead of brass. They tended to build up a little corrosion inside the stem. There used to be both short and long Schrader valve cores...I always had the best luck with the short ones. Also they used to make many Schrader valve cores out of brass but I have always preferred the stainless steel.

was 4 wheeling once. aired down or aired up I forget. one valve was leaking. I was desperate, so all I could do was push the valve open & closed a cpl time & it stopped leaking. whatever had clogged it, worked free

Get a pack of these from your auto parts store and swap the valve out from an old tube.
TR VC 2 Screwdriver Type Valve Cap - Tire caps - Tire Hardware | Miltonindustries.com

They have a version that actually is supposed to act as a seal.

Possibly, the valve may just need to be tightened.

These caps with a built in valve core wrench are available at almost any auto parts store and the auto accessory department of any big box store. I've seen some with a rubber gasket inside the cap and I think that's the type intended to slow or stop a valve leak.

That was my first thought. Try the simplest option first.

Are the bubbles coming out around the valve or through the valve? The former could mean that the valve stem is leaking at the base where it is bonded to the rest of the tube. The latter could be nothing more than a valve core that needs to be tightened up
Pay closer attention to where the bubbles are coming from

Which is why I mentioned that the valve stem could be coming in bonded to it's "rubber" jacket. Andy

I just thought that quoting the OP might emphasize that it is important to look closely at where the bubbles are coming from

I don't know what's wrong with my bike but the new tube leaked air aswell and it was a slow leak. Went to LBS and got a new tube for free, cleaned the tire and got the most dirt of the rim strip before installing the new tube. Let's see if the tire and tube are going to hold air.

With the leaky valve tube the air came out of the valve.

Whenever you buy a Schraeder tube, snug-up the valve core with a valve core wrench. Get one at the auto parts store if you don't have one. Test the core under water before you mount it to the bike (I stick it down into a cup of water) and have a few extra valve cores in your tool box and carry a couple in your seat bag too. Keep the caps on to keep the valve clean and operating correctly.

I understand that running presta and Schrader valves with the caps on goes against the grain and is (quote) "un-cool" but to heck with that. If you want to keep the valves in good shape run caps. Besides, if any rider looks down upon caps, well, it's plain stupid. Really.

Once or twice, I fixed this by removing it and reinstalling it.

Chances are, you can fish one out of the trash at your LBS.

The new tube I installed does leak air and it's really slow leak through the valve core I think. I installed the spear tube I got. Let's see if the tube is holding air like it's should tomorrow it seems to be doing that.

I'm going to buy a vale tool and see if I can fix the broken tube I got.

Simple solution, a valve core tool-schrader cap as a matter of course, is nice to have on 1 wheel , of the bicycle.