In this video I go over an example on differential equations and this time show that the solutions to the second-order differential equation y" + 9y = 0 are in the form of a combination of sine and cosine functions. This differential equation can be re-arranged to y" = -9y which is the same form as that in my last video on the motion of a spring. And thus as expected the solutions should be involving trigonometric functions because they model the oscillations of a spring very well.
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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 the functions
y = Asin(kt) + Bcos(kt)
is also a solution.
Solution
