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Question 1 (10 points)  Compute the Wronskian of the set. All steps must be shown. Then use your answer to justify whether the given set of functions is linearly independent or not.  A detailed explanation must be provided.  A value to the first part and a yes or no response to the second part is insufficient.

Question 10 (10 points)  Find the general solution of the given second-order differential equation.

Question 2 (10 points) Two-part question. The parts are distinct.  Please read each question part and answer accordingly. a. Determine whether the statement is true or false.  If it is true, explain why.  If it is false, explain why or give an example that disproves the statement.  Note: An answer that simply states “True” or “False” will earn ZERO credit.  An appropriate justification must be provided as part of the solution response.  If

Question 6 (10 points)  A 16-pound object stretches a spring 8/9 feet by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 6 inches upward from its equilibrium position and given a velocity of 1 ft/sec downward.  Find the displacement at any time t. 

Question 6 (10 points) Find the general solution (and a particular solution for the IVP) and determine whether there is any transient term in the general solution. where

Question 10 (10 points) A 24-volt battery is connected to a series circuit in which the inductance is henry and the resistance is 12 ohms. Determine the current if the initial current is zero.

Question 2 (10 points) Find an implicit general solution for the first-order ordinary differential equation.  

Question 3 (10 points) Show that the given first-order differential equation is not exact and then solve it by finding the appropriate integrating factor.

The Pacific coast of the United States is generally experiencing greater erosion than the Atlantic and Gulf coasts.

All of the following are typically characteristic of depositional shores except: