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Math Help - differential equations

  1. #1
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    differential equations

    Find a function y of x such that 4yy'= x and y(4) = 5

    y = ? (function of x)


    I approached this problems in the same way as other differential equations but have not arrived at a correct answer. I was treating y' the same as dy/dx and if this is incorrect, how and why?

    Since the variables are already separated, I integrated both sides:

    4y = x

    4y^2/2 = x^2/2
    2y^2 = x^2/2

    Then I solved for y:

    y^2 = (x^2/2) / 2
    y^2 = x^2
    y = +/- x + C
    since when x = 4, y = 5
    y = x + 1 or y = x+9

    neither of these equations are correct. Please help me figure out where I went wrong! I am new to these types of problems and my book doesn't have any examples using the y' notation so I'm not sure exactly how to approach it.

    Thanks!!
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  2. #2
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    Quote Originally Posted by littlejodo View Post
    Find a function y of x such that 4yy'= x and y(4) = 5

    y = ? (function of x)


    I approached this problems in the same way as other differential equations but have not arrived at a correct answer. I was treating y' the same as dy/dx and if this is incorrect, how and why?

    Since the variables are already separated, I integrated both sides:

    4y = x

    4y^2/2 = x^2/2
    2y^2 = x^2/2

    Then I solved for y:

    y^2 = (x^2/2) / 2
    y^2 = x^2
    That is not correct, because

    4y = x

    y = x /4

    Integrate

    1/2 *y^2 = 1/2 * x^2 /4

    multiplied by 2

    y^2 = x^2/4

    not! y^2 = x^2
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  3. #3
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    okay, thanks!

    so then y = sqrt(x^2/4) or sqrt(x^2) / sqrt(4) which is +/- x/2

    since when x = 4, y = 5, the equation needs to be
    y = x/2 + 3 ( or that is what I would think, but it is wrong)

    what did I do wrong now?
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  4. #4
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    solved

    I got it. I have a bad habit of leaving off the constant until the end.

    thanks!!!
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