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General Solution to ODE

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data
    This was a quiz problem
    Give the value of n and C for which y=Cx^n is a solution of the equation
    xdy/dx - 6y = 0


    2. Relevant equations

    ans
    n= 6
    C= 0 (some triangle symbol) an n .. ineligible mark

    3. The attempt at a solution
    n = 6
    C = All real numbers
    my tutor explained it ages ago, but now i am in stuvac i fogot why C isn't all real RE
    i have my exam tomorrow and i am just going through mistakes i have made in quizzes
     
  2. jcsd
  3. Nov 8, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Try and do it yourself. Put y=Cx^n into the left side of the ODE. How can the result be 0 for all x?
     
  4. Nov 8, 2009 #3

    Mark44

    Staff: Mentor

    This is not very complicated. Your differential equation is
    xy' = 6y and your solution is y = Cxn

    From your solution, y' = nCxn - 1, so xy' = nCxn
    From the differential equation, xy' = 6y, so nCxn = 6Cxn, so n = 6 and C can be any real number.
     
  5. Nov 8, 2009 #4
    oh great lol thats what i got n=6 and C is all RE and i got marked down...tat was 15% quiz....
     
  6. Nov 8, 2009 #5
    are u saying C is all real numbers except 0?
     
  7. Nov 8, 2009 #6
    hmm i still don't understand why C can't be zero if it is the solutions is only satisfied when y = 0 and x can be anything...

    was my tutor wrong to mark me down?
     
  8. Nov 8, 2009 #7

    Mark44

    Staff: Mentor

    No, he is not. You were saying that in your first post.
     
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