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Solving for 'k' such that some function is a solution of a diff. eq.

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Find k such that x(t)=18^t is a solution of the differential equation dx/dt=kx

    3. The attempt at a solution

    I took the derivative of x(t)

    x'= ln(18)*18^t

    then set it equal to kx,

    kx = ln(18)*18^t

    giving,

    k = [ln(18)*18^t]/x

    I am sure I am missing something simple but have not been able to figure it out.
     
  2. jcsd
  3. Sep 2, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    Your problem is here :

    ##kx = ln(18)18^t##

    You have ##x(t) = 18^t## so really you have :

    ##k(18^t) = ln(18)18^t##
    ##k = ln(18)##
     
  4. Sep 2, 2013 #3
    That's embarrassing... :)

    Thank you!
     
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