Finding the intergral function (dQ/dt) = kQ

[miniradman]

Homework Statement

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

Homework Equations

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=e^kt+e^c
Where e^c is a constant, so let e^c=A
Q=Ae^kt

∴ Q=Ae^kt

Can anyone see where I've gone wrong?

 

[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 = e^kt + e^c. 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?

You made the same mistake in your next post.

 

[miniradman]

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

e^kt+c
e^ktx e^c

right?

 

[spaghetti3451]

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

 

[miniradman]

awesome!

Thanks man, I owe you one

 

[HallsofIvy]

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

 

[miniradman]

ahhh... ok, thanks for that

 

[Mark44]

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.

 

[miniradman]

Sorry, I have terrible spelling