Suppose the Lanchester's war model:
$f'(t)=-0.5g(t)+x\sin^2(t)$
$g'(t)=-0.5f(t)+\cos^2(t)$
with $f(0)=g(0)=2$.
How to estimate how small $x$ can be in order to make $f(t)$ won't reach $0$ on the interval $[0,15]$?
By using mathematica, it's easy to solve the equations with a constant number instead of a variable $x$. But how to optimize $x$?