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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 .

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oops...I meant |y(1)(p)+y(2)`(p)|<2. –  Ester Nov 14 '12 at 9:16
$t=x$? Isn't it? –  vesszabo Nov 14 '12 at 11:58
Yes,I meant that –  Ester Nov 14 '12 at 13:03
Maybe it has something to do with Floquet theory? –  Pragabhava Nov 15 '12 at 21:00

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