# Values of the coefficients of the series involved and

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values of the coefficients of the series involved, and then (b) do obtain the the numerical values of the coefficients c 1 , ... , c 5 to the first solution, y 1 ( x ), given by Theorem 6.3 when c 0 = 1. [ Keep the parts separate. ] ______________________________________________________________________ 7. (10 pts.) Solve the following second order initial-value problem using only the Laplace transform machine.

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MAP2302/FinalExam Page 6 of 6 ______________________________________________________________________ 8. (10 pts.) (a) Given f ( x ) = x is a nonzero solution to , obtain a second, linearly independent solution by reduction of order. (b) Use the Wronskian to prove the two solutions are linearly independent. ______________________________________________________________________ 9. (10 pts.) An 8-lb weight is attached to the lower end of a coil spring suspended from the ceiling and comes to rest in its equilibrium position, thereby stretching the spring 0.4 ft. The weight is then pulled down 6 inches below its equilibrium position and released at t = 0. The resistance of the medium in pounds is numerically equal to 2x , where x is the instantaneous velocity in feet per second. (a) Set up the differential equation for the motion and list the initial conditions. (b) Solve the initial-value problem set up in part (a) to determine the displacement of the weight as a function of time. ___________________________________________________________________________ Bonkers 10 Point Bonus: Obtain a condition that implies that will be an integrating factor of the differential equation and show how to compute μ when that sufficient condition is true. Say where your work is for it won’t fit here.
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• Fall '08
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• 3 pts, 4 pts, 0.4 ft

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