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Math Help - [SOLVED] Ingegrating factors

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] Ingegrating factors

    Assign to each of the following differential equations the integrating factor/s (if there are any listed, multiple answers possible).

    A) (1 + y^2)/x^2 + y′ = 0 I) μ = 1/(1 + y^2)

    B) y/(4 + x) + y′ = 0 II) μ = 1/y

    C) 1 + (1 + x)yy′ = 0 III) μ = 4 + x


    A= I
    B= III
    C= II
    Last edited by ronaldo_07; February 4th 2009 at 01:42 PM.
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  2. #2
    Member ronaldo_07's Avatar
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    Quote Originally Posted by ronaldo_07 View Post
    A= I
    B= III
    C= II

    Can anyone confirm if this is correct?
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  3. #3
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    Quote Originally Posted by ronaldo_07 View Post
    Assign to each of the following differential equations the integrating factor/s (if there are any listed, multiple answers possible).

    A) (1 + y^2)/x^2 + y′ = 0 I) μ = 1/(1 + y^2)

    B) y/(4 + x) + y′ = 0 II) μ = 1/y

    C) 1 + (1 + x)yy′ = 0 III) μ = 4 + x


    A= I
    B= III
    C= II
    Check on what you post in (A) - it's not linear
    (B) is correct and check on your post on (C) because it has an integrating factor but not one that is list here.
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  4. #4
    Member ronaldo_07's Avatar
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    A- If its not linear then there are no integrating factors?
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  5. #5
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    Quote Originally Posted by ronaldo_07 View Post
    A- If its not linear then there are no integrating factors?
    Good point. Usually integrating factor are used for linear ODE but if you write your equation

    \frac{1+y^2}{x} \; dx + dy = 0

    then ask for \mu such that your equation becomes

    \mu \frac{1+y^2}{x} \; dx + \mu\; dy = dF = 0, then yes, you are correct.
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    What would be the integrating factor for for C, if it is not in the list?
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  7. #7
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    Quote Originally Posted by 1234567 View Post
    What would be the integrating factor for for C, if it is not in the list?
    1 + (1 + x)y y' = 0


    if you write the equation as

    dx + (1 + x)y dy = 0

    then it would be

    \mu = \frac{1}{1+x}
    Last edited by Jester; February 8th 2009 at 11:38 AM. Reason: latex typo
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  8. #8
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    Quote Originally Posted by danny arrigo View Post
    c) 1 + (1 + x)yy′ = 0


    if you write the equation as

    dx + (1 + x)y dy = 0

    then it would be

    \mu = \frac{1}{1+x}

    Thak for that, was not really sure what it could have been
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