I have a Non-Homogeneous ODE of the form $y'' + 8y' + 17y = 5$ which I have obtained the solution $y(x) = ae^{-4x}[\cos(x) + i\sin(x)] + be^{-4x}[\cos(x)-i\sin(x)] + \frac{5}{17}$ where $a$ and $b$ are complex constants.
I am unsure of how to find a constant, $c$, which satisfies the equation $z(x) = y(x) - c$ where $c$ is a real constant and $z(x)$ is a Homogeneous Differential Equation. I originally thought that $c = \frac{5}{17}$ but that seems too simple.
How should I go about finding $c$?