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Homework Help: Differential equation

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve the ODE, 4(dy/dx)=4-y^2

    2. Relevant equations



    3. The attempt at a solution

    separating the variables,

    dy/(4-y^2)=dx/4

    then integrating both sides

    (1/4) ln((2-y)/(2+y))=x/4+c

    Multiply by 4, so now the constant is different, so must i use a different variable for the constant?

    ie ln((2-y)/(2+y))=x+c'

    (2-y)/(2+y)=(e^x)(e^c')

    y=(2-2(e^x)(e^c'))/((e^x)(e^c')+1)

    then here, 2(e^c') is another constant, do i have to use another variable to represent it?

    And also what's the definition of arbitrary constant?
     
  2. jcsd
  3. Jun 30, 2010 #2

    Mark44

    Staff: Mentor

    Yes.
    Above, e^c' is just a constant, so you can replace it by, say A.
    That's a good idea.
    When you evaluate an indefinite integral such as this --
    [tex]\int x~dx = \frac{1}{2}x^2 + C[/tex]
    -- the constant C can be any number, so can't be determined, hence is arbitrary.
     
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