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

  • Thread starter mesa
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  • #1
mesa
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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.
 

Answers and Replies

  • #2
STEMucator
Homework Helper
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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)##
 
  • #3
mesa
Gold Member
687
25
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!
 

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