Find all values of A so that y=sin(Ax) is a solution to ((d^2)y)/(d(x^2))+9y=0, A constant.

Question

calculus question, PLEASE HELP.

Answer 1

 

d²y/dx² + 9y = 0  ;  dy/dx = Acos(Ax) ; d²y/dx² = -A² sin(Ax)

 

-A² sin(Ax) + 9 sin(Ax) = 0  <----> (9 - A²) sin(Ax) = 0

 

(3 - A)(3 + A) sin(Ax) = 0

 

The values of A that make y = sin(Ax) a solution to the differential equation are 3, -3, and 0