Question

For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = â16y? (Enter your answers as a comma-separated list.)K = ______

Answer 1

16/81

Explanation:

Given the expression, 81y'' = -16y where y = coskt,

We want to know the value of k that satisfies the expression

y' = -ksinkt

y" = -k²coskt

Substitute y and y" into the expression given;

81y'' = -16y

81(-k²coskt) = -16(kcoskt)

-81k = -16

Divide both sides by -81

-81k/-81 = -16/-81

k = 16/81

Hence the value of k is 16/81