Differential Equations

so i have a funtion u(t) where u"+bu'=a.  b and a are both constants.  is this even solvable?  its for my physics 325 class and i'm drawing a complete blank.

First solve u" + bu' = 0
characteristic equation: r^2 + r = 0
So, r = 0 or r = -1
The complementary solution is therefore:
y_c = C_1 e^(-t) + C_2
Since a is a constant, this equation will suffice. Fill in the boundary values and solve C_1 and C_2.