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Homework Help: Solving ode

  1. Aug 13, 2010 #1
    hey i am stuck on this question for my ode course its using frobunius

    4. show that the equation

    yii + 1/x yi + (1-1/(4*x^2))y = 0

    has a regual point at x=0
    using the method of frobenius assuming a solution of the form

    y=[tex]\sum[/tex] ar xc+r

    show that the idical equation is c^2=1/4

    thanks for nay help given
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 13, 2010 #2


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    What have you managed so far?
  4. Aug 13, 2010 #3
    i have proved that x=0 is a singular point and i rearanged the ode to get

    x^2 yii + x y^i + x^2 y -1/4 y =0

    however trying to work out coeff of xr , xr+1 etc etc is the probelm because i get

    a0*(r^2-0.25) = 0

    and i thought u would have ot get a a0 in the equation for a1
  5. Aug 13, 2010 #4


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    The r's in your equations should be c's, but otherwise they look okay.

    If you solve for the coefficients for r≥2, you'll see they depend on the either a0 or a1.
  6. Aug 13, 2010 #5


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    Because this 0 is a "regular singular point" for this problem, you cannot use the standard power series. You will have to use "Frobenious' method"- try something of the form
    [tex]y= \sum_n a_nx^{n+c}[/tex]

    Choose c so that a0 is NOT 0.
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