- I'd like to try it.
- I'd like to test it.
- I'd like to experiment it. (This sentence is problematic => use "experiment with")
There's a shared meaning, but we can't say they mean the same thing.
1. try: engage or put to use for some purpose. Has the broadest (including vague and casual) sense.
2. test: apply an action/stimulus to something to check its soundness, features, etc. Implies clearly defined purpose and expectations.
3. experiment: apply actions/stimuli under a careful plan to verify or discover something new. Implies more rigorous and methodical approach than "test".
"try" and "test" are primarily transitive, while "experiment" is intransitive.
So you see sentences like:
- Try that new coffee machine to see if it works.
- Test that new coffee machine and see if it's in good order.
- Experiment WITH that new coffee machine and see if it really does all that they claim it does.