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Euler Differential Equation

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve the euler differential equation

    [tex]\x^{2}y^{''}+3xy'-3y=0[/tex]
    [tex]
    \int_X f = \lim\int_X f_n < \infty
    [/tex]
    by making the ansatz [tex]y(x)=cx^{m}[tex], where c and m are constants.

    3. The attempt at a solution

    [tex]y(x)0=c^{m}[tex]
    [tex]y^{'}(x)=cm^{m-1}[tex]
    [tex]y^{''}(x)=cm(m-1)^{m-2}[tex]

    [tex]m(m-1)+3m-3=0[tex]
    [tex]m^2+2m-3=0[tex]
    [tex](m-1)(m+3)=0[tex]
    [tex]m=-3 or m=1[tex]

    Is this the solution or can c be found?
     
    Last edited: Apr 19, 2009
  2. jcsd
  3. Apr 19, 2009 #2
    Latex isn't working on this post so here it is without Latex:

    1. The problem statement, all variables and given/known data
    Solve the euler differential equation

    x^{2}y''+3xy'-3y=0

    by making the ansatz y(x)=cx^{m}, where c and m are constants.

    3. The attempt at a solution

    y(x)=cx^{m}
    y'(x)=cmx^{m-1}
    y''(x)=cm(m-1)x^{m-2}

    m(m-1)+3m-3=0
    m^2+2m-3=0
    (m-1)(m+3)=0
    m=3 or m=-1

    Is this the solution or can c be found?
     
    Last edited: Apr 19, 2009
  4. Apr 19, 2009 #3

    Astronuc

    User Avatar

    Staff: Mentor

    Latex maybe out due to technical problems.

    Is one sure of the function before the y' term - 3x^{2}?
     
  5. Apr 19, 2009 #4
    *Correction made* :)
     
  6. Apr 23, 2009 #5
    This was merely a typo, the orignal problem still remains...
     
  7. Apr 26, 2009 #6
    so....er...c?
     
  8. Apr 26, 2009 #7
    since no innitial conditions were given i shall take irt that c cannot be found.
     
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