I am almost completely lost with this problem.

I say almost completely because i have a vague understanding of the principle but my professor rushed through this lecture and our text book doesnt cover this.

Here is the problem:

Prove that every solution of the equation:

y'' + a1y' + a2y = 0 (a1 = const; a + 2 = const)

is bounded on [0, infinty) if and only if the real parts of the characteristic roots are non-positive and the roots with zero real part have multiplicity 1.

Any guidance on this would be appreciated.