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$a\left( t\right)$ 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

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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. – Babak S. Jan 9 '13 at 14:24

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