# Differential Equation

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#1

Hi, can someone explain why, in part b, when taking things to their respective sides, in order to integrate them, the markscheme takes 20 to the P side - basically forming 20/(P(5-2P)). I find this really confusing as in part A it asks u to find partial fractions of 1/ P(5-2P) , and in literally every question I’ve seen where it asks u to do something beforehand, u always use that to ur advantage in the next part of the question, so I only bought the P(5-2P) to the other side, and left the right hand side as 1/20, but got the answer wrong.
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4 weeks ago
#2
You can turn 20/(P(5-P)) in to 20(1/(P(5-P))) and then since 20 is just a constant you can move it outside of the integral and then you are just left to integrate 1/(P(5-P)). Then like you said you use part a.) to split it into partial fractions so you have two easy ln integrals. I dont see any reason why your method wouldn't produce the right answer however so you must have made an error at some point in your working or the mark scheme was wrong. I imagine the reason the 20 was moved as well is whenever you can remove fractions from an equation you should as it makes things a bit more clear, in this particular case it doesn't matter very much though.
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#3

Do you mind explaining to me where I’ve gone wrong ? I’ve subbed in the right things and I’m fairly certain my maths it right (?) but I’m getting a negative number for weeks. Markscheme started off with taking 20 to the other side as well, but I wanna try getting to the answer by leaving 20 on the RHS, as that is what I’d probably do in the exam. Thanks.
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3 weeks ago
#4
Looks like you double count the 5 multiplier when integrating the (5-2p) term?
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3 weeks ago
#5
it is up to you whether you move the 20. the answer has to come out the same.
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#6
(Original post by mqb2766)
Looks like you double count the 5 multiplier when integrating the (5-2p) term?
Which line is this ?
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#7
Ohh I’ve just integrated it again, and got -ln(5(5-2P)). I’ll try the question again now
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#8
Nah still can’t manage it lmao
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#9
Ahaha I managed it, thank you very much
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3 weeks ago
#10
Ahaha I managed it, thank you very much
Well done - been asleep. You can see why it's easier to make mistakes when using frsctions (original reply)?
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#11
Yep definitely. Think I’m just gonna eliminate fractions whenever possible from now on - saves so much time and effort.
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