function x(t) on [0, ∞) is satisfied with next differential equation
\begin{equation} \frac{dx}{dt} =( -a + b(t))\:x + c(t) \\ \end{equation}
Additionaly, a is defined positive constant.
And then , if continuous function b(t), c(t) is satisfied with below,
\begin{equation} \lim_{t \to \infty} b(t) = \lim_{t \to \infty } c(t) = 0 \end{equation}
Please prove that next equality is satisfied \begin{equation} \lim_{t \to \infty} x(t) = 0 \end{equation}