An inductor in an electric circuit has voltage operating as

This week, we study Laplace Transforms, one of the most useful transforms in all of mathematics, because they allow us to move from the “differential equation” space or domain to an algebraic domain, operate algebraically to a solution, and then transform back into differential equation space to provide the answer.Throughout the Lab, show all your intermediate steps.

First, some review questions.

1.) 

 for a 4 H inductor. Find the current in the circuit after 10 seconds if the initial current is 575 mA.  (Note: use as the base for your calculations.)

2.)  Find the first 5 terms of the sequence:,n = 1,2,3,4, and 5. (Pay attention to the values of n in this case)

3.)  Find the Taylor Series approximation for  where and

4.)  Solve the differential equation   First question: which method are you going to use to solve it?

5.)Find the particular solution of the differential equation satisfying the given conditions,if

Use the following table to find the transforms needed for problems 6-10.

TABLE OF LAPLACE TRANSFORMS

6.)  Find the LaPlace Transform of the given function.

7.)  Find the inverse LaPlace Transform of the given function.

8.)       Expand the LaPlace transform of the given expression in terms of x and .  Do not solve.

9.)  Solve the following differential equation using LaPlace Transforms.

10.)               Solve the following differential equation using LaPlace Transforms.

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Higher order homogeneous and non-homogeneous Differential Equations, with distinct, repeated, or complex roots

Show all work for full credit.

1.)        In your electronics classes, you will utilize the following ODE to solve for various quantities for a given class of circuits. 

Given  and , find the general solution to the given ODE. 

2.)        Find the general solution to the ODE

3.)        Find the general solution to the ODE

4.)        Find the general solution to the following ODE:

5.)    Find the particular solution of the differential equation satisfying the initial conditions  and .The given ODE is

6.)    Find the particular solution of the differential equation satisfying the given conditions      

7.)        Find the general solution for:

8.)  Find the general solution of the ODE

9.)  Whatvalue must the variable “b” take on if the equation is critically damped?

10.)  For a given radio tuning circuit, .  Find the equation relating the charge and the time, given