Find the general solution of the given differential equation, and use it to determine how
solutions behave as t→∞.
y' − 2y = 3et
The Attempt at a Solution
After some work, I got y=-3et+ce2t . 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 cant 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?