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Differential equations again

  1. Jan 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that sines and cosines are the solutions of the differential equation

    f''(x) = (-σ^2)f(x)

    What if a boundary condition is included that g(0) = 0?


    2. Relevant equations
    f''(x) = (-σ^2)f(x)


    3. The attempt at a solution
    Plugging in sin(σx) and cos(σx) yields an equality therefore the expression is true.

    I'm just confused about the boundary condition.

    If g(0) = 0 then only the sin(σx) works, correct?
     
  2. jcsd
  3. Jan 13, 2013 #2
    I am assuming that g(0) = 0 stands for f(0) = 0.

    The solution f(x) = sin(σx) satisfies the condition that f(0) = 0 for all values of σ. But the solution f(x) = cos(σx) satisfies the given condition only for particular values of σ.
     
  4. Jan 13, 2013 #3

    SammyS

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    I hope you mean f(0) = 0 .

    Yes, if f(0) = 0, then only sin(σx) works.

    cos(σx) does not work for that boundary condition.

    @grzz,

    For what value of σ will cos(σ∙0) = 0 ?
     
  5. Jan 13, 2013 #4
    Thanks SammyS for pointing out my mistake.

    The last part of my post i.e.'But the solution f(x) = cos(σx) satisfies the given condition only for particular values of σ' is not correct.
     
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