# Finding the intergral function (dQ/dt) = kQ

## Homework Statement

Find the integral (I think I'm finding the integral) of:
$\frac{dQ}{dt}$ =kQ

## 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:

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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?

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

ekt+c
ektx ec

right?

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

awesome!

Thanks man, I owe you one

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

ahhh... ok, thanks for that

Mark44
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.

Sorry, I have terrible spelling 