A damped vibration experiment is modeled by the following IVP: y + 6y + 13y = 0; y(0) = 4, y(0) = 4.

Solve the above IVP by first finding the General Solution to y''+6y'+13y=0 and then express its solution in the form of Ae^at*cos(bt), where A > 0 and < . Identify A,a,b and .

Please show all work and steps clearly, so I can follow your logic and learn to solve similar ones myself. I will rate your answer and provide feedback. Thank you kindly!