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    (Original post by TheLifelessRobot)
    Here you go.
    Thanks!
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    I can't believe this exam is tomorrow, feels just like a mock or something, huh...

    I think FP3 is a super hard unit but the papers get extremely easy over time when you know what you're doing because each paper has extremely similar questions.
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    (Original post by Emi1998)
    how do you tell the difference between

    y= Acosnx + Bsinnx for the complementary function from dy^2/dx^2 +n^2y

    and y= Ae^-nx +Be^nx.

    If you have
    dy^2/dx^2 +n^2y , this will give k^2= +/- ni , so because it isn't real is it y=Acosx + Bsinx

    dy^2/dx^2 -n^2y this will give k^2= n^2, so because it is real, is it y= Ae^(nx) +Be^(-nx)


    Is this correct
    This is correct. You if you have complex roots to the auxiliary equation then you could write the complementary function as  y_{gs} = \text{A}e^{(a+bi)x} + \text{B}e^{(a-bi)x} but if you use the fact that  e^{ix} 0 \cos x + i\sin x you will see that the conplementary function simplifies down to  y= e^{ax}( \text{A} \cos bx + \text{B} \sin bx) .
    [Note. The arbitrary constants, A and B in the first and second complementary function I gave are not necessarily the same.]
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    Has anyone got any tips for avoiding silly mistakes? It seems as though that's where I'm loosing most of my marks

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    (Original post by JPencil)
    Has anyone got any tips for avoiding silly mistakes? It seems as though that's where I'm loosing most of my marks

    Posted from TSR Mobile
    Practice, even so you will still make them, but fewer
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    If a 2nd order DE is set equal to a polynomial such as 3x + 4, is the trial function supposed to be ax + b or ax^2 + bx + c?
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    (Original post by TheLifelessRobot)
    If a 2nd order DE is set equal to a polynomial such as 3x + 4, is the trial function supposed to be ax + b or ax^2 + bx + c?
    Former.
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    Hey guys, any predictions regarding the paper? I've found 2014 No8 quite weird any other tricky questions to look at?
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    (Original post by TheLifelessRobot)
    If a 2nd order DE is set equal to a polynomial such as 3x + 4, is the trial function supposed to be ax + b or ax^2 + bx + c?
    Though you can try ax^2 +bx +c to be sure but you will see coeficient of x^2 will be 0 so a will be 0
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    Can someone give me a link for those legacy papers with polar coordinates
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    2014 q8 b(ii) i dont understand the mark scheme? Diagram anyone?
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    (Original post by XxswagmasterxX)
    Hey guys, any predictions regarding the paper? I've found 2014 No8 quite weird any other tricky questions to look at?
    Im stuck on that question, any help?
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    (Original post by TheLifelessRobot)
    If a 2nd order DE is set equal to a polynomial such as 3x + 4, is the trial function supposed to be ax + b or ax^2 + bx + c?
    Depends. If there is no term in y, say you have
     \displaystyle \frac{\text{d}^2y}{\text{d}x^2} + 3\frac{\text{d}y}{\text{d}x} = 12x+16 ,
    a trial function of  px+q would not work in this case.
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    (Original post by misslili118)
    Im stuck on that question, any help?
    I just done that question but it's a bit messy Name:  image.jpg
Views: 144
Size:  491.5 KB lol if u can even read that
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    (Original post by Hjyu1)
    I just done that question but it's a bit messy Name:  image.jpg
Views: 144
Size:  491.5 KB lol if u can even read that
    how did u get the sin(pi --(pi/6 +a)) part I don't understand
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    (Original post by misslili118)
    how did u get the sin(pi --(pi/6 +a)) part I don't understand
    never mind just understood it
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    (Original post by misslili118)
    how did u get the sin(pi --(pi/6 +a)) part I don't understand
    It's a triangle so all the angles add up to 180 degrees so pi radians and u already know 2 angles which are pi/6 and Alpa so you take them away from pi to get your missing angle then do sine rule
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    (Original post by Hjyu1)
    It's a triangle so all the angles add up to 180 degrees so pi radians and u already know 2 angles which are pi/6 and Alpa so you take them away from pi to get your missing angle then do sine rule
    why can't you just use alpha and 1 with pi/6 and root21 /9 for the sin rule
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    What is the perfect answer for the question asking about why it is an improper integral? Are they picky on the language you use for those answers?
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    (Original post by B_9710)
    Depends. If there is no term in y, say you have
     \displaystyle \frac{\text{d}^2y}{\text{d}x^2} + 3\frac{\text{d}y}{\text{d}x} = 12x+16 ,
    a trial function of  px+q would not work in this case.
    Would it be best just to use a trial function with a degree of n+1 if the DE is set equal to a polynomial of nth degree just to be safe?
 
 
 
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