Core Maths 4: Differential equations

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    Hi there

    Please could someone take a loko at the below and for question 4, tell me why I am getting a slightly different answer to whats in the book, and for question 5, explain how to do this as I have completely gone off the rails lol

    I am really struggling with these types of questions, so if anyone can give me a little Differential equations for dummies guide or point me in the direction of one, I would be most grateful, cheers;


    Question 4:



    Question 5:





    Many thanks
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    First one: How on Earth are you getting exponentials? Separate the variables and integrate!
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    first one:

    integral 1/h^1/2 dh = integral k dt

    where do you get exp from?
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    Second one is no better.

    \int \frac{1}{x-x^2} \, dx \neq - \ln |x-x^2| + c

    Factorise the denominator of the integrand and split it into partial fractions.
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    1/(x(x-1) does integrate to ln(x(x-1)

    you need to split it into partial fractions.
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    lol,there is an echo is this thread
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    And I can only echo too

    OP you seem to have misunderstood this topic completely

    You do not even begin correctly

    \frac{dh}{dt} = -k\sqrt{h}
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    (Original post by TenOfThem)
    And I can only echo too

    OP you seem to have misunderstood this topic completely

    You do not even begin correctly

    \frac{dh}{dt} = -k\sqrt{h}
    I ignored that as the negative sign can be incorporated within the constant of proportionality. Think the other problems are more glaring!
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    (Original post by Mr M)
    Think the other problems are more glaring!
    Agreed
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    ok thank you all for your replies.

    I have managed to solve question 5, but am still having trouble with question 4.

    With question 4, is this going in the right direction;

    2√h = -kt + c

    4h = (-kt)² + c

    h = 1/4(-kt)² + c

    ???

    Then does, c = 200?
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    (Original post by jackie11)
    ok thank you all for your replies.

    I have managed to solve question 5, but am still having trouble with question 4.

    With question 4, is this going in the right direction;

    2√h = -kt + c

    4h = (-kt)² + c

    h = 1/4(-kt)² + c

    ???

    Then does, c = 200?
    (a + b)^2 \neq a^2 + b^2
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    (Original post by jackie11)
    ok thank you all for your replies.

    I have managed to solve question 5, but am still having trouble with question 4.

    With question 4, is this going in the right direction;

    2√h = -kt + c

    4h = (-kt)² + c

    h = 1/4(-kt)² + c

    ???

    Then does, c = 200?
    Definitely going in the right direction, but I'm not convinced on your workings between lines 1 and 2 as you should square all of the right hand side as well. I know that a constant squared is just another constant, but you should also get -2ckt which you haven't got. Therefore, I would just substitute some values into the top line to find values for k and c. I think that works out fine.
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    (Original post by Quip)
    Definitely going in the right direction, but I'm not convinced on your workings between lines 1 and 2 as you should square all of the right hand side as well. I know that a constant squared is just another constant, but you should also get -2ckt which you haven't got. Therefore, I would just substitute some values into the top line to find values for k and c. I think that works out fine.
    ok how about this;

    2√h = -kt + c

    when h = 200, t = 0

    2√200 = c

    when h = 128, t = 5

    2√128 = -5k + 2√200
    2√128 - 2√200 = -5k
    -5.656 = -5k
    5.656 = 5k
    1.13 = k
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    (Original post by jackie11)
    ok how about this;

    2√h = -kt + c

    when h = 200, t = 0

    2√200 = c

    when h = 128, t = 5

    2√128 = -5k + 2√200
    2√128 - 2√200 = -5k
    -5.656 = -5k
    5.656 = 5k
    1.13 = k
    If this is still relevant, yes that's right (I think), but it may be more useful to keep k as a surd though.
 
 
 
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