Which variable is used to denote the current? What is the relevant differential equation for the cumnt?

DE questions
Write up neat, organized solutions to ALL problems ON YOUR OWN. Be sure to include acknowledgment of anyone who you worked with or received help from.
Problem 1 For what positive values of b do. y°(t) + by'(t) + 4y(t) = 0 have solutions that are overdamped oscillators? Explain.
Problem 2 An inductor (L =1 II) and resistor (R = 0.1 Ohms) are joined in series with a voltage source with E(t) = 10 — 2t volts. If there is no current at time t = 0, find an expression for the current in the circuit at time t. Hint: Go back to the handout on circuits. Which variable is used to denote the current? What is the relevant differential equation for the cumnt?
Problem 3 Find the inverse Laplace Transforms, by manipulating the functions to match a form in our table.
(a) Y(,) = — rft (b) Y(s) (,t1) ‘2F4 (c) Y(s) =

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