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Math Help - Homogeneous de

  1. #1
    Newbie
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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. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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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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