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Another ODE substution method

  1. Feb 9, 2009 #1

    tony873004

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    This is another example from the blackboard that I'm trying to understand.

    [tex]\frac{{dy}}{{dx}} = \frac{{x^2 + 3xy + y^2 }}{{x^2 }}[/tex]

    Divide through by x^2
    [tex]\frac{{dy}}{{dx}} = 1 + \frac{{3y}}{x} + \left( {\frac{y}{x}} \right)^2 [/tex]

    make substitution
    [tex]let\,\,v = \frac{y}{x}[/tex]

    Therefore,
    [tex]y = vx\,[/tex]

    But the next step in the example says
    [tex]y = vx\frac{{dy}}{{dx}} = v\frac{{dv}}{{dx}}[/tex]

    How did the dy/dx pop in there?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 9, 2009 #2

    Dick

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    Your 'copying from the blackboard' is wildly inaccurate. Why don't you just try to solve it without trying to verify inaccurate notes? If y=v*x, dy/dx=x*dv/dx+v.
     
  4. Feb 9, 2009 #3

    tony873004

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    Thanks, Dick. That got me through the rest of the problem.
     
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