# How to find the C satisfied $\left| y\left( t\right) \right| < Ct$

$a\left( t\right)$ is a continuity function on $R^{+}$ (x>0), $y\left( t\right)$ is a function satisfied the equation $y''+a\left( t\right)y=0$, if $\int _{0}^{+\infty }t|a\left( t\right)|dt < \infty$，prove there exist a C>0 (C is a constant)，such that if $t\in R^{+}$ and t is large enough, $|y\left( t\right)|\leq Ct$.

I don't know where to start ,how to use the differential equation

-
Write $y$ as an integral of $y'$. Then integrate by parts to create $y''$ there. Then use the equation. – user53153 Jan 9 '13 at 14:03
@PavelM.Thanks, I will try it later. – Jebei Jan 9 '13 at 14:05
See this link. I think it inspires us for the question. en.wikipedia.org/wiki/Big_O_notation – Babak S. Jan 9 '13 at 14:24