For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' =

y' =

y' = kcos(kt)

Now for y''

y'' =

y'' =

y'' =

Hence, the equation y'' + 144y = becomes

+

∴

±

±

∴ or

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12