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

1. Sep 2, 2013

### mesa

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. Sep 2, 2013

### Zondrina

Your problem is here :

$kx = ln(18)18^t$

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

$k(18^t) = ln(18)18^t$
$k = ln(18)$

3. Sep 2, 2013

### mesa

That's embarrassing... :)

Thank you!

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