We use experience as a verb when something happens to us, or we feel it. It is rather formal:
I experienced a feeling of deep sadness as I entered the refugee camp.
Customers have experienced problems in finding parking places at the mall.
We don’t use live instead of experience:
How children behave when they grow up depends on what they experience during early childhood.
what they live during early childhood.
Experiment as a verb means ‘try something in order to discover what it is like or to find out more about it’:
Scientists have experimented with liquids and gels in which plants can grow artificially.
I wish the government would stop experimenting with new teaching methods for our kids every couple of years.
We don’t use experiment when we are talking about feelings or things which happen:
She suddenly experienced a sensation of homesickness.
experimented a sensation…
The company’s Asia branch experienced a sharp drop in profits in 2007.
experimented a sharp drop…