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How to find two constants in an equation

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    i'm trying to find two constants in the same equation. its an initial value problem

    there's a two parameter family x=c1cost+c2sint with initial conditions x''+x=0, x(pi/6)=1/2, and x'(pi/6)=0

    so i'm trying to find c1, and i equate the problem to 1/2 and subsitute the t's for pi/6, so it looks like


    which of course equals sqrt(3)c1/2 + c2/2

    but how do i get the values of c1 and c2? i've tried everything and i need them to find a solution

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 28, 2008 #2
    well, you already found one relation sqrt(3)c1/2 + c2/2=1/2, to find another relation,

    take the first derivative of x=c1cost+c2sint, and apply the second contidion that you are given x'(pi/6)=0

    so you'll get two lin. eq in two unknowns, c1,c2, and u should be able to solve it.
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