Diff-EQ: non-zero k so y = sin(kt) satisfies y'' + 9y = 0

Limits, differentiation, related rates, integration, trig integrals, etc.
stellar
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Diff-EQ: non-zero k so y = sin(kt) satisfies y'' + 9y = 0

Postby stellar » Tue Jun 23, 2009 6:59 pm

For what nonzero values of "k" does the function y = sin(kt) satisfy the differential equation y" + 9y = 0 ?

Do I do the derivative twice, and plug it in?

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stapel_eliz
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Postby stapel_eliz » Wed Jun 24, 2009 12:14 am

That should do it:

y = sin(kt)

y' = k*cos(kt)

y" = -k^2*sin(kt)

Then y" + 9y is -k^2*sin(kt) + 9*sin(kt) = (9 - k^2)(sin(kt)).

For what values of "k" will this equal zero? :wink:


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