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Math Help - Differential equation

  1. #1
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    Differential equation

    I am currently studying differential equations and stumbled upon this problem:

    \frac{dy}{dx} = \frac{3x^2}{2y + cos(y)}, y(0) = pi

    Any help is much appreciated,

    Dranalion
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  2. #2
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    It's a separation of variables. Basically cross multiply and integrate.
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  3. #3
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    I have solved to here:

    (2y + cos(y))dy = (3x^2)dx

    \int (2y + cos(y))dy = \int (3x^2)dx

    y^2 + sin(y) = x^3 + c

    How do I get y by itself (as a function of x)
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  4. #4
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    Quote Originally Posted by Dranalion View Post
    I have solved to here:

    (2y + cos(y))dy = (3x^2)dx

    \int (2y + cos(y))dy = \int (3x^2)dx

    y^2 + sin(y) = x^3 + c

    How do I get y by itself (as a function of x)
    You can't.

    The best you can do is get an explicit function x(y).


    x = \sqrt[3]{y^2 + \sin{y} + C}.


    Now use your initial condition to find C.
    Last edited by mr fantastic; October 24th 2009 at 04:54 AM. Reason: Fixed a latex tag.
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