TITLE: Limit of y(x) in Second Order Differential Equation
QUESTION [6 upvotes]: So, even though I know how to solve ODEs, I don't know how I should proceed about this question:
Let $a$, $b$, and $c$ positive constants. If $y = y(x)$ is solution to the differential equation $ay'' + by' + cy = 0$, then $\lim_{x\to\infty}$ $y(x)$:
(a) doesn't exist and tends to $+\infty$. 
(b) exists and is $0$. 
(c) doesn't exist and tends to $-\infty$. 
(d) exists and is $\pi$. 
(e) exists and is $e$.
I tried to take the limit of the possible solutions but even if $a$, $b$, and $c$ are positive-only numbers, there are many possibilities so I couldn't achieve anything.
Thanks for the reading!

REPLY [4 votes]: Always check for the trivial solution.  $y \equiv 0$ is a solution of the given equation.  This makes answer (b) correct.  (The other correct answers here arrive at the same conclusion by other means.)