Solving DE with Constant: Homogenous & Non-Homogenous

[phiby]

My math is a little rusty - so please bear with me if this is a stupid question.

I know how to solve both homogenous and non-homogenous DEs

However, I am not sure where a DE with a constant falls & how to solve it.

For eg.

y'' + 2y' + c = 0
(c is a constant).

You cannot convert this into an algebraic equation in r like you do for regular homogenous DEs. So what's the method for solving this?

If this is a different category of DEs (i.e. neither homo nor non-homo), then even giving me the name of this type of DE is good enough - I can google and find the method.

An example of this type of DE is a bar loaded with a uniformly distributed load of f.
The DE is

AEu'' + f = 0

u -> deflection.

f is a constant.

 

[Charles49]

You can solve the equation y'' + 2y' = -c. This is a non homogenous equation where the non-homogenous part is a constant. So the general solution is

-((c x)/2) - 1/2 exp(-2 x) C[1] + C[2]

where C[1] and C[2] are constants.