Show that the equation $ \frac{d^2\space y} { d\space x^2}+ y\sin^2 (100t)=0 $ has only bounded solutions.
I was trying to prove $|y(1)(p) + y(2)(p)|< 2$ where $y(1)$ and $y(2)$ are $2$ linearly independent solutions and $p$ is the period of $\sin^2 (100t)$.
Any help will be appreciated .