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4 years ago
#7
Thanks very useful
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4 years ago
#8
In FP2 where are series?
Nevermind they are really easy
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4 years ago
#9
Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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#10
(Original post by simonli2575)
Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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maybe a typo or a mistake

I will check later

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#11
(Original post by simonli2575)
Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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I did look at the question and I am afraid I cannot see the problem
Can you be a bit more specific so if it is wrong I can change it
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4 years ago
#12
(Original post by TeeEm)
I did look at the question and I am afraid I cannot see the problem
Can you be a bit more specific so if it is wrong I can change it
In question 5, the particular integral is divided by x.

I also remember that my teacher told me the particular integral doesn't change when doing 2nd order ODEs, but why? And why not in question 5?

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#13
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#14
(Original post by simonli2575)
In question 5, the particular integral is divided by x.

I also remember that my teacher told me the particular integral doesn't change when doing 2nd order ODEs, but why? And why not in question 5?

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Sorry but I do not follow
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4 years ago
#15
(Original post by TeeEm)
Sorry but I do not follow
Question 3:
You find that the general solution is
v = y/x = Ae^2x + Be^-2x - e^x
But when you multiply both sides by x, this becomes
y = Axe^2x + Bxe^-2x - e^x
In which e^x is not multiplied by x, and is also a particular integral.

Similarly, in question 5:
You find that the general solution is
u = xy = Ae^-3x + Bxe^-3x + 3x - 2
However, this time when both sides are divided by x, you get
y = A/x*e^-3x + Be^-3x + 3 - 2/x
In which the particular integral, 3x - 2, has been changed.
My question is, do all particular integrals remain unchanged during substitution? If so, why? If not, why not?

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#16
(Original post by simonli2575)
Question 3:
You find that the general solution is
v = y/x = Ae^2x + Be^-2x - e^x
But when you multiply both sides by x, this becomes
y = Axe^2x + Bxe^-2x - e^x
In which e^x is not multiplied by x, and is also a particular integral.

Similarly, in question 5:
You find that the general solution is
u = xy = Ae^-3x + Bxe^-3x + 3x - 2
However, this time when both sides are divided by x, you get
y = A/x*e^-3x + Be^-3x + 3 - 2/x
In which the particular integral, 3x - 2, has been changed.
My question is, do all particular integrals remain unchanged during substitution? If so, why? If not, why not?

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which booklet are you looking at?
is it this one?
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4 years ago
#17
(Original post by TeeEm)
which booklet are you looking at?
is it this one?
Yes.

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#18
(Original post by simonli2575)
Yes.

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there are no questions in this booklet to match what you are saying
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4 years ago
#19
(Original post by TeeEm)
there are no questions in this booklet to match what you are saying
Sorry, I meant this one.

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1
#20
I found the questions now.
The PI will not change if it is a function say of the independent variable (say x) and the substitution used transforms the dependent variable (say y)
if you get a question like this in your exam you just follow the instructions!
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