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Solving an ODE

  1. Aug 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Ay'+Bxy=Cy
    y=f(x)
    A,B,C are real constants
    3. The attempt at a solution
    This kinda looks like a Bernoulli equation but not really.
    I thought about using an integrating factor but there is function of x on the right side.
    If I tried undetermined coefficients what would my guess function be.
     
  2. jcsd
  3. Aug 26, 2012 #2
    It seems like you could solve this by first manipulating to get [tex]y' + \frac{Bx-C}{A}y = 0[/tex] at which point you now have an ODE of the form [tex]y' + P(x)y = Q(x)[/tex] and there is a general way to solve such ODEs.
     
  4. Aug 26, 2012 #3
    where Q(x)=0 and then use an integrating factor.
     
  5. Aug 26, 2012 #4
    Yep, seems like that oughta work
     
  6. Aug 27, 2012 #5
    if you do that you get y=0.
     
  7. Aug 27, 2012 #6

    ehild

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    or [tex]y' = -\frac{Bx-C}{A}y [/tex]

    which is separable. [tex]\frac{y'}{y} = -\frac{Bx-C}{A}[/tex].

    ehild
     
  8. Aug 27, 2012 #7
    wow cant believe I missed that , thanks for the help
    ok so I would get
    [itex] ln(y)= \frac{-1}{A}(\frac{Bx^2}{2}-Cx)+F [/itex]
    F= integration constant
    then I just raise each side to e and I will have y
     
  9. Aug 27, 2012 #8

    ehild

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    Exactly. It will be a bit simpler if you eliminate the minus sign in front of the parentheses,

    [tex]\ln(y)=\frac{1}{A}(Cx-B\frac{x^2}{2})+F[/tex]

    ehild
     
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