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Determining linearity

  1. Jul 6, 2011 #1
    So I just started taking an intro diff eq course and here's one of my hw problems:

    "Determine whether the given first-order diff eq is linear in the indicated dependent variable."

    (y2-1)dx + xdy=0; in y; in x

    I got the whole bit about the general form for linearity but I was thrown off by having just a 'dx' and 'dy' instead of the more familiar 'dy/dx'

    (answer to the question is non linear when y is dependant, linear when x is dependant)

    I'm confused as to what exactly 'dy' or 'dx' means, both conceptually and mathematically. I have a feeling there's a nice thread on this somewhere...

    thanks for the help!
     
  2. jcsd
  3. Jul 6, 2011 #2
    Please note forum policy on homework.

    https://www.physicsforums.com/showthread.php?t=88061

    Having said that here is a hint.

    [tex]\begin{array}{l}
    \left( {{y^2} - 1} \right)dx = - xdy \\
    \left( {1 - {y^2}} \right)dx = xdy \\
    \frac{{dy}}{{dx}} = \frac{{\left( {1 - {y^2}} \right)}}{x} \\
    \frac{{dx}}{{dy}} = \frac{x}{{\left( {1 - {y^2}} \right)}} \\
    \end{array}[/tex]

    Can you see which has x as the dependent variable and which has y?
     
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