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# C4 Differential equation help Watch

1. http://www.ocr.org.uk/Images/59547-q...athematics.pdf

Question 9ii)

For the constant c I get ln140 in the mark scheme it says -ln140 I can't seem to figure out why.

My working out :

1 / ( 160 - theta) d theta = k dt

ln ( 160 - theta) = kt + c

When t = 0 theta = 20

ln140 = 0 + c
2. (Original post by IShouldBeRevising_)
http://www.ocr.org.uk/Images/61388-q...hematics-2.pdf

Question 9ii)

For the constant c I get ln140 in the mark scheme it says -ln140 I can't seem to figure out why.

My working out :

1 / ( 160 - theta) d theta = k dt

ln ( 10 - theta) = kt + c

When t = 0 theta = 20

ln140 = 0 + c
you missed a minus sign when you integrated the LHS!
3. (Original post by davros)
you missed a minus sign when you integrated the LHS!

I don't understand
4. (Original post by IShouldBeRevising_)
http://www.ocr.org.uk/Images/59547-q...athematics.pdf

Question 9ii)

For the constant c I get ln140 in the mark scheme it says -ln140 I can't seem to figure out why.

My working out :

1 / ( 160 - theta) d theta = k dt

ln ( 160 - theta) = kt + c

When t = 0 theta = 20

ln140 = 0 + c
Temperature is increasing so:
5. (Original post by joostan)
Temperature is decreasing so:

You can say k, but then you must remember that k is a negative constant.
The question says increasing ?
6. (Original post by IShouldBeRevising_)
The question says increasing ?
ah, misread the q COMPLETELY! poor show see above.
7. (Original post by IShouldBeRevising_)
The question says increasing ?
Allow me to try again.

what does 160-theta differentiate to?
8. (Original post by joostan)
Allow me to try again.

what does 160-theta differentiate to?
-1 ?
9. (Original post by IShouldBeRevising_)
-1 ?
So as davros says - where is the minus on the LHS?
f'(x)/f(x) = -1/(160-theta)
So the integral should read -[-1/(160-theta)]
10. (Original post by joostan)
So as davros says - where is the minus on the LHS?
f'(x)/f(x) = -1/(160-theta)
So the integral should read -[-1/(160-theta)]
But originally the lhs = 1/160 - thetA

d/dx(1/ 160 - theta ) = -1 however the original lhs is 1 not -1?
11. (Original post by IShouldBeRevising_)
But originally the lhs = 1/160 - thetA

d/dx(1/ 160 - theta ) = -1 however the original lhs is 1 not -1?
when you integrate 1/(160 - theta) you should get -ln|160 - theta|

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