Question about solutions of $x''+(1+r(t))x=0$ when $\int_1^\infty |r(t)| dx <\infty$ .

Question

Let $x''+(1+r(t))x=0$ where $r(t)$ is continous and $\int_1^\infty |r(t)| dx <\infty$ show that the equation has solutions $\phi_1$ and $\phi_2$ such that $$\lim_{t\to\infty} [(\phi_1(t)-e^{it})=0$$ and $$\lim_{t\to\infty} [(\phi_1'(t)-ie^{it})=0$$ and $$\lim_{t\to\infty} [(\phi_2(t)-e^{-it})=0$$ and $$\lim_{t\to\infty} [(\phi_2'(t)+ie^{-it})=0$$

I don't know how to start to solve. I need some hint.

thanks.