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Math Help - Integrating to Find Particular Solution

  1. #1
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    Integrating to Find Particular Solution

    Firstly,

    I keep getting a LaTex Error with the following equation:
    y=\int(x+\frac{20}{x^2}+\frac{5}{x^2})dx

    Secondly, my teacher said the answer to the following question is c=3.9, but I keep getting a different answer:

    Integrate the following equation to find the particular solution
    y= integral of (x + 20/x^3 + 5/x^2)dx, where x = 3 and y = 9
    Here is my working:

    y = [(x^2)/2] + [(20x^-2)/-2] + [(5x^-1)/-1] + C

    y = [(x^2)/2] - (10x^-2) - (5x^-1) + C

    y = [(x^2)/2] - (10/x^2) - (5/x) + C

    9 = [(3^3)/2] - (10/3^2) - 5/3 + C

    9 = 4.5 - 1.1 - 1.6 + C

    9 - 4.5 + 1.1 + 1.6 = c

    C = 7.2 (My teacher's answer is C=3.9)

    What did I do wrong with LaTex, and this answer?
    Last edited by sparky; April 25th 2011 at 11:38 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Certainly

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  3. #3
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    Quote Originally Posted by sparky View Post
    Firstly,

    I keep getting a LaTex Error with the following equation:
    y=\int(x+\frac{20}{x^2}+\frac{5}{x^2})dx

    Secondly, my teacher said the answer to the following question is c=3.9, but I keep getting a different answer:



    Here is my working:

    y = [(x^2)/2] + [(20x^-2)/-2] + [(5x^-1)/-1] + C

    y = [(x^2)/2] - (10x^-2) - (5x^-1) + C

    y = [(x^2)/2] - (10/x^2) - (5/x) + C

    9 = [(3^3)/2] - (10/3^2) - 5/3 + C

    9 = 4.5 - 1.1 - 1.6 + C
    3^2= 27, not 9, so3^2/2= 12.5, not 4.5.

    9 - 4.5 + 1.1 + 1.6 = c

    C = 7.2 (My teacher's answer is C=3.9)

    What did I do wrong with LaTex, and this answer?
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  4. #4
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    Sorry, 9 = [(3^3/2] - (10/3^2) - 5/3 + C

    is supossed to be 2, my mistake:

    y = [(x^2)/2] - (10/x^2) - (5/x) + C

    9 = [(3^2)/2] - (10/3^2) - 5/3 + C

    9 = 4.5 - 1.1 - 1.6 + C

    9 - 4.5 + 1.1 + 1.6 = c

    C = 7.2



    Quote Originally Posted by FernandoRevilla View Post
    Certainly

    Yes, this is what I got as well. So what is the correct answer?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sparky View Post
    Sorry, 9 = [(3^3/2] - (10/3^2) - 5/3 + C

    is supossed to be 2, my mistake:

    y = [(x^2)/2] - (10/x^2) - (5/x) + C

    9 = [(3^2)/2] - (10/3^2) - 5/3 + C

    9 = 4.5 - 1.1 - 1.6 + C

    9 - 4.5 + 1.1 + 1.6 = c

    C = 7.2





    Yes, this is what I got as well. So what is the correct answer?
    Making my calculator do all the work so I'm not making a trivial numerical error, I get 7.2.

    -Dan
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