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

## 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 Helper

## 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.

##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)##

• 1 person

##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!