Find all numbers r, real and complex, such that e^rx is a solution. Find two linearly independent real solutions.
(D^2 + 9)y = 0
Here's how I tried to solve it:
1. r^2 + 3^2 = 0
2. r^2 = -3^2
3. r = ±3i
So two independent linear solutions would be: cos 3y and sin 3y
Does this look about right?