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Struggling with Differential Equations

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi, I'm struggling with a differential equations:


    2. Relevant equations

    3. The attempt at a solution




    then I get confused because of the derivative.

    I thought it could be
    y'e^(-sinx)=d/dx(e^(-sinx)y) but that clearly doesnt work...
  2. jcsd
  3. Feb 15, 2010 #2


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    Separation of variables might be a good approach here... you can show that the solution is given by

    [tex]\int \frac{1}{1 - y} \, dy = \int \cos(x) \, dx[/tex]

    and both of the integrals are well calculable.
  4. Feb 15, 2010 #3


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    If you want to use an integrating factor, you need to move the y's to the same side.

    [tex]y'+(\cos x)y = \cos x[/tex]

    When you multiply through by the integrating factor p(x), the LHS becomes the derivative of p(x)y(x).

    [tex]\mbox{LHS} = p(x)y'(x)+p'(x)y(x) = [p(x)y(x)]'[/tex]

    That's where the y' term goes.
  5. Feb 15, 2010 #4
    Gah! My bad :( I feel quite stupid now... The exercise is on integrating factors and I didn't see that o_O
    Thanks vela for clearing up integrating factors for me :D

    so to continue...



    1-y=Ae^(-sinx), A=e^c


    which according to the solution is correct. Thanks guys! It's actually an IVP but I'll just leave that out since it's easy.
  6. Feb 15, 2010 #5


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    Note that what you are doing now is separation of variables.
    To use integrating factors, you should proceed along vela's lines.
  7. Feb 15, 2010 #6
    I did note that, it's just easier this way. Thanks CompuChip
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