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Factoring question

  1. Mar 1, 2008 #1
    When trying to solve a higher order differential equation, how can I factor it to find the general solution. A question like :[tex]y^{(4)}-4y^{(3)}+6y^{(2)}-4y^{(1)}+y=0[/tex].
    So I can write this as:[tex]m^4-4m^3+6m^2-4y^1=0[/tex]. How can I factor m? The prof mentioned something about Pascal's Triangle, but I'm not sure what to do, I haven't even looked at Pascals Triangle in I dont even know how many years.
  2. jcsd
  3. Mar 1, 2008 #2
    Did you mistype something, please check it again.

    Here is Pascal's Triangle.


    The first equation you gave, in binomial form is: [tex](y-1)^4=y^4(-1)^0+4y^3(-1)^1+6y^2(-1)^2+4y^1(-1)^3+y^0(-1)^4=y^4-4y^3+6y^2-4y+1[/tex]

    Do you see the pattern?
    Last edited: Mar 1, 2008
  4. Mar 1, 2008 #3
    Yeessss, I suppose
  5. Mar 1, 2008 #4
    (y+1)^1=y+1=1 1
    (y+1)^2=y+2y^2+1=1 2 1
    (y+1)^3=y^3+3y^2+3y+1=1 3 3 1

  6. Mar 1, 2008 #5
    Thanks Alot!
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