# Asymptotic Behavior of Solutions to Linear Equations

That is the title to the problem I am stuck on. Here is what it says..

Consider the equation,

$$\frac{dy}{dx} + ay = Q(x)$$

where a is positive and Q(x) is continuous on $$[0,\infty ],$$

Show that the general solution to the above equation can be written as..
$$y(x) = y(x_{0})e^{-a(x-x_{0})}+e^{-ax}\int^{x}_{x_{0}}e^{at}Q(t)dt$$

Where $$x_{0}$$ is a non-negative constant
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This part is easy, I just differentiated y(x) and plugged it into the equation. My real struggle is in the next part.
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If $$|Q(x)|\leq k for x\geq x_{0}$$ where k and $$x_{0}$$ are non-negative constante, show that..

$$|y(x)|\leq |y(x_{0})|e^{-a(x-x_{0})}+\frac{k}{a}[1-e^{-a(x-x_{0})}], for x\geq x_{0}$$
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The only thing I can come up with at the moment is plugging in the expression for y(x) and using the triangle inequality. I don't know where it would lead me though..