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Differential equation

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=27900&stc=1&d=1283196761.jpg

    2. Relevant equations



    3. The attempt at a solution

    If my solution is right please tell me why I should omit [tex] 2xe^{-x}+0.5e^{2x} [/tex]
     

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  3. Aug 30, 2010 #2

    vela

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    You shouldn't omit the particular solution. The initial conditions apply to the complete solution, not just the homogeneous solution.
     
  4. Aug 30, 2010 #3
    So the solution of my book is wrong as I expected!

    In this case we have
    [tex] c_{1}=4 c_{2}=-4.5 c_{3}=0 [/tex]
     
  5. Aug 30, 2010 #4

    vela

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    They can't all be 0 otherwise you'd have y(0)=1/2.
     
  6. Aug 30, 2010 #5
    Do you know how to solve ODEs with Laplace Transform? it is perfectly suited for constant coefficient ODEs with starting conditions at x=0.
     
  7. Aug 30, 2010 #6
    This is a very good advice. I'd take it, in case you know Laplace Transforms.
     
  8. Aug 30, 2010 #7

    vela

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    Really? I wouldn't. I find using Laplace transforms for a problem like this is usually more tedious than solving it using the method of undetermined coefficients.
     
  9. Aug 30, 2010 #8
    Depends if you want to solve the inverse LT by hand. :)
     
  10. Aug 30, 2010 #9
    But then you have to find the 3 constants that solve the IVP.
    and if you solve by Laplace Transform you will find them along the way.

    Nevertheless, both ways are good !
    and you better know how to solve if by different methods.

    Also learn Lagrange's Variation of Parameters, it's a little longer but it's ingenious ! :)
     
  11. Aug 30, 2010 #10

    vela

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    But with the Laplace transform, you'll need to do a partial fractions decomposition, so you end up having to solve a system of linear equations anyway.

    I agree it's good to know both ways. It's kind of neat to see it all work out with Laplace transforms, but once you do it a few times, the novelty wears off. ;)
     
  12. Aug 31, 2010 #11
    Thank you very much for your kind help. I know Laplace but I have to revise it now.

    I actually solved it again and I got the same results:
    [tex] c_{1}=4 c_{2}=-4.5 c_{3}=0 [/tex] I mean again [tex] c_{3}=0 [/tex]
     
  13. Aug 31, 2010 #12

    vela

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    Obviously, you're doing something wrong. Why don't you post your work so we can see where the problem is?
     
  14. Aug 31, 2010 #13
    attachment.php?attachmentid=27910&stc=1&d=1283244074.jpg
     

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  15. Aug 31, 2010 #14

    vela

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    Oh, you did get the right answer. It's just that your equations ran together, so it looked like you got c1=4c2=4.5c3=0 so that all of the coefficients were 0.

    If you're going to use LaTeX for something like that, you should put the equations on separate lines. :)
     
  16. Aug 31, 2010 #15
    Dear vela, thank you very much for your great generosity!

    Dear PhysicsForums thank you very much for your fabulous website!
     
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