ODE y''+b^2 y=0 where b is vector

[mogul]

Hi,
please help me with this task. I'm wondering what is the right result.
I have a ODE
$y'' - b^2 y =0$

also the result should be
$y=C e^{\pm bx}$

but what is the result when b is vector?
$\vec b=(b_x, b_y)$

is this the result?
$y=C e^{\pm \vec{b}x}$

or this?
$y=C e^{\pm |b| x}$

how to solve it?
thanks for help!

 

[HallsofIvy]

If b is a vector, then what do you mean by "$b^2$"? The dot product? Then coefficient is the square of the length of the vector.