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Differential equation nonzero value problem

  • Thread starter Gauss177
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  • #1
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Homework Statement


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.

Homework Equations




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.
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
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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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