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

[mesa]

Homework Statement

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

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.

 

[STEMucator]

Homework Statement

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

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.

Your problem is here :

$kx = ln(18)18^t$

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

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

 

[mesa]

Your problem is here :

$kx = ln(18)18^t$

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

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

That's embarrassing... :)

Thank you!