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?

Thanks,

Jim