- #1

ehabmozart

- 213

- 0

## 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 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?