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Which method for this DE?

  1. May 11, 2004 #1
    I'm new to DEs, and can do most I've come across so far, but this has me stumped:


    Out of these methods which should I use?

    1 Integrating Factor
    2 Seperable
    3 Bernoulli
    4 Change of Variable (y=xv)

    I'm pretty sure it's the 4th but I've not been able to find a solution. Could someone confirm that this is the correct approach?
  2. jcsd
  3. May 11, 2004 #2


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    Basically, yes, however:
    You'll remain stumped as long as you do not "eliminate" the constants in your expression (that would be +4 in the numerator, -2 in the denominator).

    In order to eliminate these constants in an acceptable manner, use the following trick:
    Find the solutions [tex]x_{0},y_{0}[/tex] of the linear system:


    This yields: [tex]x_{0}=0,y_{0}=2[/tex]
    Now change the scales:
    [tex]\hat{x}=x-x_{0}, \hat{y}(\hat{x})=y(x)-y_{0}[/tex]

    In the hatted variables, you now have the differential equation:

    This should help you solve the problem..
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