Solving $\frac{dy}{dx} = ae^{-bx} - cy(x)$ How would you solve an equation in the form
$$\frac{dy}{dx} = ae^{-bx} - cy(x) $$
where $a, b, c$ are just constants. My ultimate goal is to find $y(x)$ without the derivative in there. 
My confusion comes from the fact that the right hand side has both $y(x)$ and $x$ itself in it. I tried using the integrating factor method and it gets me a similar form of solution that I want, but not completely. So is this the method I should be using or is there another that works for this type of equation?

Hint :
It is :
$$y'(x) + cy(x) = ae^{-bx}$$
Find an integrating factor $\mu$ as 
$$\mu(x) = \exp\left( \int c\mathrm{d}x\right) = e^{cx}$$
and multiply both sides of the ODE with it. It yields :
$$e^{cx}y'(x) + ce^{cx}y(x) = ae^{cx-bx} $$
Now, observe that :
$$e^{cx}y'(x) + cy(x) = \Big( e^{cx}y(x) \Big)'$$
Can you finish ?
