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Thread: Homogeneous de

  1. #1
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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
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    $\displaystyle
    \begin{gathered}
    \frac{{dy}}
    {{dx}} = \frac{{y + x}}
    {{y - x}} \hfill \\
    \Leftrightarrow \frac{{dy}}
    {{dx}} = \frac{{\frac{y}
    {x} + 1}}
    {{\frac{y}
    {x} - 1}} \hfill \\
    \end{gathered} $

    now make the following substitution:

    $\displaystyle
    v = \frac{y}
    {x} \Rightarrow v + x\frac{{dv}}
    {{dx}} = \frac{{dy}}
    {{dx}}$

    ....
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