An electrical circuit consisting of a resistor, capacitor, inductor, and a batte

Question

An electrical circuit consisting of a resistor, capacitor, inductor, and a battery in series can be modeled by the following initial value problem:

where L, R, and C are constants.

c) What type of differential equation did you end up with? Be as specific as possible.

d) Write and solve the characteristic equation (auxiliary equation) for your differential equation from (b). (Your answers should be complex numbers).

e) Find two linearly independent solutions to the differential equation from (b) and use them to create a general solution.

h)  Use your UC Functionto find a particular solution to the non-homogeneous differential equation in part (g).

Explanation / Answer

by using laplace transform we can easily find this..

first use the lapalce for conversion into s domain and next apply connditoons to go t

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