Another Mathie Christmas Carol

What Function's This?

(To the tune of "What Child Is This?")

What function's this? When added to
c times its derivative gives me
An f(t), oh how can we
Solve this first order DE?

Sometimes we can separate
Then take both sides and integrate
'Else, we can find I(t)
Then multiply and it's easy

Sometimes, and this is what we hate
The last two things won't be working
But with constants c, it's still easy
We can solve this without hurting

First we find y_h(t)
Which will solve it homogeneously
Then a particular integral
Gives us the full solution.

SquirrelToken
Hoping I pass DEs this term