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Thread: Homogeneous de

  1. November 4th 2008, 04:33 AM #1
    skirk34
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    Homogeneous de

    I need help solving the homogeneous de

    dy/dx=(y+x)/(y-x)

    Thxs in advance
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  2. November 4th 2008, 05:08 AM #2
    Peritus
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    <br /> \begin{gathered}<br /> \frac{{dy}}<br /> {{dx}} = \frac{{y + x}}<br /> {{y - x}} \hfill \\<br /> \Leftrightarrow \frac{{dy}}<br /> {{dx}} = \frac{{\frac{y}<br /> {x} + 1}}<br /> {{\frac{y}<br /> {x} - 1}} \hfill \\ <br /> \end{gathered}

    now make the following substitution:

    <br /> v = \frac{y}<br /> {x} \Rightarrow v + x\frac{{dv}}<br /> {{dx}} = \frac{{dy}}<br /> {{dx}}

    ....
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