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Homework Help: Differential equation nonzero value problem

  1. Feb 20, 2007 #1
    1. The problem statement, all variables and given/known data
    a) For what nonzero values of k does the function y = sin kt satisfy the differential equation y" + 9y = 0?

    b) For those values of k, verify that every member of the family of functions y = A*sin kt + B*cos kt is also a solution.

    2. Relevant equations

    3. The attempt at a solution
    I'm a little confused on what I need to do here. I can do problems where you have to show that every member of a family of functions is a solution of a differential equation (differentiate the function, then plug in the function into the differential equation, and see if they are the same). But I don't see how to use that in this problem.

    Thanks for the help.
  2. jcsd
  3. Feb 20, 2007 #2


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    Staff Emeritus
    Science Advisor

    Well, why not try differentiating the function, and plugging it into the equation. This will give you a condition for k such that y=sinkt is a solution.
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