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DE problem involving limits

  1. Oct 9, 2013 #1
    1. The problem statement, all variables and given/known data

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

    y' − 2y = 3et



    2. Relevant equations

    DE

    3. 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?
     
  2. jcsd
  3. Oct 9, 2013 #2

    haruspex

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    e2t will beat et, so it will go to positive or negative infinity according to the sign of c.
     
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