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Math Help - Integration help

  1. #1
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    Jun 2008
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    Integration help

    Hi everyone

    I have some homework due in a day and i can't understand this question...

    consider the differential equation: 2xy(dy/dx)=y^2-9, x≠0

    1a) find the steady state solutions(if any)

    b) find the general solution

    c) Find the particular solution satisfying y=5 when x=4

    Any help would be appreciated thanks already!
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  2. #2
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    Melbourne Australia
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    Part a can be solved fairly easily by understanding that a "steady state solution" means that dy/dx=0. So substitute dy/dx=0 into the equation and solve it for y.

    For the rest of the question, first check that you have copied it down correctly. A well placed minus sign would make the problem very much easier!
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  3. #3
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    <br />
2xy\dfrac{dy}{dx} = y^2 - 9<br />
    <br />
\Rightarrow \dfrac{2ydy}{y^2 - 9} = \dfrac{dx}{x}<br />
    <br />
\\\Rightarrow \ln(y^2 - 9) = \ln x + C<br />
    <br />
\\y^2 - 9 = xe^C<br />
    <br />
\\y^2 = 9 + xe^C<br />
    <br />
\\y = \pm \sqrt{9 + xe^C}<br />
    sub in the numbers and you get
    <br />
\\y = \sqrt{9 + 4x}<br />
    Last edited by jjzshen; June 17th 2008 at 03:39 AM. Reason: trying to figure out what this syntax error is...
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