RLC Circuit Source Transformation
You're not meant to have 2 independent sources working at the same time in the circuit, so the best way to deal with this is to use source transformation which will produce a voltage source making the circuit a combination of 2 voltage sources. I'm not sure it can be solved otherwise. Besides before you solve for neper frequency the RLC circuit has to be either a completely parallel or series circuit. Your circuit above is neither (series-parallel), to find 'alpha' you have to use source transform to make it a completely series circuit.