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Math Help - Diff. Eq. change of variable

  1. #1
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    Diff. Eq. change of variable

    y ' = x + y

     u = x + y

    We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

    \frac{du}{dx} = dx + y

    \frac{du}{dy} = x + dy

    Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find \frac{dy}{dx}, but I can't seem to find that in terms of u and x.
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  2. #2
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    Quote Originally Posted by diablo2121 View Post
    y ' = x + y

     u = x + y

    We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

    \frac{du}{dx} = dx + y

    \frac{du}{dy} = x + dy

    Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find \frac{dy}{dx}, but I can't seem to find that in terms of u and x.
    Hi

    I suppose u and y are functions of x
    \frac{du}{dx} = 1 + \frac{dy}{dx} and \frac{dy}{dx} = x + y

    So \frac{du}{dx} = 1 + u
    This is a 1st order differential equation

    I hope this will help you
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