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C4 help- Differential Equations

Hi,

Doing a retake so haven't touched the content in 6 months so do bear with me :smile:

How did it go from line 2 to line 3 in the screenshot?

I got line 2, but I have different signs for line 3.

I Have ln(5000-N)= kt- ln(t) +c whereas this is different to the correct answer.

Thanks for any help in advance
Screen Shot 2017-12-27 at 21.40.03.png47.8KB
Reply 1
Avatar for Notnek
Notnek
21
Original post by Xphoenix
Hi,

Doing a retake so haven't touched the content in 6 months so do bear with me :smile:

How did it go from line 2 to line 3 in the screenshot?

I got line 2, but I have different signs for line 3.

I Have ln(5000-N)= kt- ln(t) +c whereas this is different to the correct answer.

Thanks for any help in advance

What's the derivative of ln(5000-N)?
The integral of 1/u is ln|u|. Notice derivative of 5000-N is -1 hence it's -1 times ln|u|; -ln|5000-N| follows.

I suggest re-learning C4 integration; https://www.examsolutions.net/a-level-maths/edexcel/c4-tutorials/
Original post by Xphoenix


I Have ln(5000-N)= kt- ln(t) +c whereas this is different to the correct answer.

Thanks for any help in advance


∫15000−NdN=−∫−15000−NdN\displaystyle \int \frac{1}{5000-N} dN = -\int \frac{-1}{5000-N} dN

and NOW you can apply your ln. (since the numerator is the derivative of the denominator.)
Reply 4
Avatar for Xphoenix
Xphoenix
OP
18
Ah of course:
-1 and divide by the derivative.
Original post by Notnek
What's the derivative of ln(5000-N)?


Thanks for pointing it out

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