Hi

given the nonhomogeneous linear differential-equation

$\displaystyle x'(t) + a(t) x(t) = b(t)$

with

$\displaystyle a: [0, \infty[ \rightarrow [0,\infty[,$

$\displaystyle b: [0, \infty[ \rightarrow [0,\infty[ $

and no explicit solution x(t) of the problem, i like to show that

$\displaystyle x(t) \rightarrow 0.$

in addition for $\displaystyle t \rightarrow \infty$ i'm able to show that:

$\displaystyle a(t) \rightarrow 0$ and $\displaystyle b(t) \rightarrow 0$

do you know any theory i'm allowed to use in this case? i just find some results in stabilitytheory for homogeneous case with a constant coefficient a(t).

thanks for any hints or suggestions in advance.

kind regards, debelix