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anonymous

  • 5 years ago

d^2f/dx^2+(ax+b)df/dx+cf=const Could someone know an easier way to solute this ode?

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  1. anonymous
    • 5 years ago
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    reduce to a quadratic and solve for roots by quadratic formula

  2. anonymous
    • 5 years ago
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    What do you mean with "reduce to a quadratic " ? Do you mean, I should transform it in dies form d^2f/dx^2+bdf/dx+cf=const-(ax+b)df/dx .

  3. anonymous
    • 5 years ago
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    if you allow the coefficients to be the terms for a quadratic, i.e. \[r ^{2}+(ax+b)r+c = 0\] then use the quadratic formula \[(-b \pm \sqrt{b ^{2}-4ac})/2a\] to find r such that it satisfies the ODE

  4. anonymous
    • 5 years ago
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    but you can't do that because r is also a function of x. r=r(x)

  5. anonymous
    • 5 years ago
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    no you treat it as a constant

  6. anonymous
    • 5 years ago
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    what do you have so far for your work and/or proof?

  7. anonymous
    • 5 years ago
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    I though about another approach, please, have a look on this site, http://www.ltcconline.net/greenl/courses/204/PowerLaplace/seriesSolutions1.htm

  8. anonymous
    • 5 years ago
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    did you figure out the u substitution? if you did then it should follow...but i honestly don't think you need to use series for it

  9. anonymous
    • 5 years ago
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    I figure it, but it seems to be really complicatet to have a serie solution.

  10. anonymous
    • 5 years ago
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    Because of the non-constant coefficients and it become very ugly

  11. anonymous
    • 5 years ago
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    can I send you a copy of my work?

  12. shadowfiend
    • 5 years ago
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    Try uploading a pic to http://imgur.com/ and pasting the link to it here.

  13. anonymous
    • 5 years ago
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    yeah i would like to see it

  14. shadowfiend
    • 5 years ago
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    (We'll be adding image upload to OpenStudy soon, I hope.)

  15. anonymous
    • 5 years ago
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    You could try using laplace transforms. It would turn the the 2nd order ODE into a 1st order ODE. Usually 1st order ODE are easier to solve. Look at the example here http://tutorial.math.lamar.edu/Classes/DE/IVPWithNonConstantCoefficient.aspx

  16. anonymous
    • 5 years ago
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    i think that's what he was trying to do

  17. anonymous
    • 5 years ago
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    here is a copy http://imgur.com/9y7hu

  18. anonymous
    • 5 years ago
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    hope u can read it,

  19. anonymous
    • 5 years ago
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    ok yeah now it is better to see... i think that it works, after simplifying then you can solve the ODE. but i think its already simplified...

  20. anonymous
    • 5 years ago
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    but when it is already simplified, what is the result now?

  21. anonymous
    • 5 years ago
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    I'm gonna use matlab to solve,

  22. anonymous
    • 5 years ago
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    you can also check your answer on this website: http://www.wolframalpha.com/input/?i=y''+%2B+(ax%2Bb)y'%2Bcy+%3D+f The answer seems a bit complicated :\

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