Thread: values which satisfy diferential equation

Find all values of k for which the function y=sin(kt) satisfies the differential equation y''+16y=0. Separate your answers by commas.

Anyone know what the values or are?

y=sinkt
y'=kcoskt
y''=-k^2sinkt

y''+16y=0

essentially (-k^2sinkt) = (-16sinkt)

so k=+-4?????

ya and 0

Er 0 is a trivial case, actually...