Second order linear non-homogenous differantial equations with costant coefiicients?

Question

How can i find a general solution for these kind of odes

Note:
The non homogenous term is also constant

Answer 1

If ay´´+by´+cy= k where k is a constant
1) find the general solution of the homogeneous equation
(it is y= C_1 e^px +C_2 e^qx where p and tue are the root of
ar^2+br+c=0)
A particular solution of the non homogenuos equation would be
y=k/c
so the general solution is
y=C_1 e^px+ C_2 e^qx +k/c