# C3/C4/FP2/FP3,M1,M2,M4,M5 Resources and links

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http://madasmaths.com/archive/maths_...expansions.pdf

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_...stitutions.pdf

http://madasmaths.com/archive/maths_...stitutions.pdf

**TeeEm**)**In the following links there are resources for the FP2 EDEXCEL****TAYLOR & McLAURIN**http://madasmaths.com/archive/maths_...expansions.pdf

**INEQUALITIES**http://madasmaths.com/archive/maths_..._questions.pdf

**COMPLEX NUMBERS**http://madasmaths.com/archive/maths_..._questions.pdf

**POLAR COORDINATES**http://madasmaths.com/archive/maths_..._questions.pdf

**1st ORDER ODEs**http://madasmaths.com/archive/maths_..._questions.pdf

**2nd ORDER ODEs**http://madasmaths.com/archive/maths_..._questions.pdf

**1st ORDER ODEs WITH SUBSTITUTIONS**http://madasmaths.com/archive/maths_...stitutions.pdf

**2nd ORDER ODEs WITH SUBSTITUTIONS**http://madasmaths.com/archive/maths_...stitutions.pdf

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Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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**simonli2575**)Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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I will check later

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**simonli2575**)

Why is it that in Question 3 of 2nd Order ODE, the particular integral doesn't change?

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Can you be a bit more specific so if it is wrong I can change it

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#12

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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

**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

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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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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**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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#15

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Sorry but I do not follow

**TeeEm**)Sorry but I do not follow

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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(Original post by

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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**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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is it this one?

http://madasmaths.com/archive/maths_..._questions.pdf

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#17

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which booklet are you looking at?

is it this one?

http://madasmaths.com/archive/maths_..._questions.pdf

**TeeEm**)which booklet are you looking at?

is it this one?

http://madasmaths.com/archive/maths_..._questions.pdf

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http://madasmaths.com/archive/maths_..._questions.pdf

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#19

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there are no questions in this booklet to match what you are saying

http://madasmaths.com/archive/maths_..._questions.pdf

**TeeEm**)there are no questions in this booklet to match what you are saying

http://madasmaths.com/archive/maths_..._questions.pdf

http://madasmaths.com/archive/maths_...stitutions.pdf

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I found the questions now.

The PI will not change if it is a function say of the independent variable (say

if you get a question like this in your exam you just follow the instructions!

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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