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DE problem involving limits

  • Thread starter ehabmozart
  • Start date
  • #1
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Homework Statement



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

y' − 2y = 3et



Homework Equations



DE

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?
 

Answers and Replies

  • #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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