Values of the coefficients of the series involved and

Info icon This preview shows pages 5–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern