What is the Behavior of Solutions of a DE with Limits as t Approaches Infinity?

[ehabmozart]

Homework Statement

Find the general solution of the given differential equation, and use it to determine how
solutions behave as t→∞.

y' − 2y = 3e^t

Homework Equations

DE

The Attempt at a Solution

After some work, I got y=-3e^t+ce^2t . Now I have problems in getting the limit as t goes to infinity. C can possibly be a positive or negative value. In case it is -ve, the answer goes to negative infinity. If it is positive, I can't really figure out what would the limit be. In the book however, it is written that 'It follows
that all solutions will increase exponentially'. HOW?

 

[haruspex]

e^2t will beat e^t, so it will go to positive or negative infinity according to the sign of c.