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Math Help - seperation of variables

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    seperation of variables

    dx/x=dy/(x+y)

    Seperation of variables is not straight forward here. I have solved in maple and get y=(ln(x) + c1)*x. Since this is a fluids class I can use maple for the hw. How do you do this by hand. Is it a substitution type seperation of variables?
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  2. #2
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    Quote Originally Posted by MarionButler View Post
    dx/x=dy/(x+y)

    Seperation of variables is not straight forward here. I have solved in maple and get y=(ln(x) + c1)*x. Since this is a fluids class I can use maple for the hw. How do you do this by hand. Is it a substitution type seperation of variables?
    Re-write your DE as

     <br />
\frac{dy}{dx} = \frac{x+y}{x} = \frac{y}{x} + 1<br />

    We can do this two ways

    1) Homogeneous: If you let y = xu the DE will separate

    2) if we write the DE as  <br />
\frac{dy}{dx} - \frac{y}{x}= 1<br />
this is linear with a integrating factor of \frac{1}{x}.
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