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Math Help - Integrating dy/dx

  1. #1
    Senior Member Paze's Avatar
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    Integrating dy/dx

    I'm getting into differential equations and I am currently watching this video while trying to solve some problems: https://www.khanacademy.org/math/dif...tial-equations

    He ends up with

    (1-y^2)dy=x^2\cdot dx

    and says: "now we can integrate".

    Why can't I simply integrate dy/dx? I'm not completely oblivious as to what is going on, but I'm just trying to get the details right.

    Thanks!
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  2. #2
    MHF Contributor

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    Re: Integrating dy/dx

    What do you mean by "simply integrate dy/dx"? And with respect to what variable? I imagine you started with \frac{dy}{dx}= \frac{x^2}{1- y^2}.

    You could write this as \int\frac{dy}{dx}dx= \int\frac{x^2}{1- y^2}dx. It is, of course easy to integrate on left to get just "y". But how are you going to integrate on the right? This is NOT a partial derivatives problem so you cannot just treat "y" like a constant- it is an unknown function of x so you cannot integrate it with respect to x.
    Thanks from topsquark and Paze
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  3. #3
    Senior Member Paze's Avatar
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    Re: Integrating dy/dx

    I see. Thanks !
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