1. Sep 11, 2013 #1

   oneamp

   

   I have, from the textbook:
   
   dy/dt = ry
   
   So I solve and get y = e^(rt)+C
   
   However, the book says that y=y_0 * e^(rt), where y_0 is the answer to the initial condition, y(0).
   
   I don't get it. The + C should be what we use to solve for the initial condition; how does y_0 end up in the same term with the exponential?
   
   Thanks

    

   oneamp, Sep 11, 2013
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3. Sep 11, 2013 #2

   bigfooted

   

   integrating dy/y=rdt leads to ln(y)=rt+C
   
   this leads to y=exp(rt+C)
   but exp(rt+C)=exp(C)*exp(rt)
   and you simply replace the constant exp(C) by a new constant C
   
   EDIT: your mistake was most likely that you didn't include the constant of integration immediately after integrating, but after getting rid of the logarithm.

    

   bigfooted, Sep 11, 2013
4. Sep 11, 2013 #3

   oneamp

   

   Yes! I see. Thank you.

    

   oneamp, Sep 11, 2013

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