Finding the intergral function (dQ/dt) = kQ

1. Apr 27, 2012

1. The problem statement, all variables and given/known data
Find the integral (I think I'm finding the integral) of:
$\frac{dQ}{dt}$ =kQ

2. Relevant equations

3. The attempt at a solution
I just got feedback from my teacher, and he told me I make a mistake somewhere in this question. But I don't know where I've gone wrong?

$\frac{dQ}{dt}$=kQ
$\frac{dQ}{Q}$=kdt
∫$\frac{dQ}{Q}$=∫kdt
lnQ=kt+c
Q=ekt+ec
Where ec is a constant, so let ec=A
Q=Aekt

∴ Q=Aekt

Can anyone see where I've gone wrong?

Last edited: Apr 27, 2012
2. Apr 27, 2012

spaghetti3451

If you substitute your solution back into the differential equation, the LHS equals the RHS, so the solution is fine. However, you wrote in an intermediate calculation that Q = ekt + ec. It can't be an addition. Try and think why it can't be an addition.

Hint: What are rules for algebraic operations with indices?

3. Apr 27, 2012

oh... Kt + c will have to go to

ekt+c
ektx ec

right?

4. Apr 27, 2012

spaghetti3451

Yup, I can't see any other mistakes. This answer should score full marks now.

5. Apr 27, 2012

awesome!

Thanks man, I owe you one

6. Apr 27, 2012

HallsofIvy

Staff Emeritus
Technically, there is one other error. The integral, $\int (1/Q)dQ= ln|Q|$, not ln(Q).

7. Apr 28, 2012

ahhh... ok, thanks for that

8. Apr 28, 2012

Staff: Mentor

Minor point: there is no such word as "intergral" in the English language. Seeing as you have started two threads with this in the title, I thought I should point it out.

9. Apr 28, 2012