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Solve It!

  1. Apr 11, 2003 #1
    I have decided to post an exercise and see what happens. You can post your own problems, too, if you wish. Have fun with this one!


    Solve the following differential equation:

    y′′′ = y
     
  2. jcsd
  3. Apr 11, 2003 #2
    y(t) = a*exp(b*t) where b^3 = 1.
     
  4. Apr 11, 2003 #3

    dg

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    The general solution is of the form

    y(x)=c1*exp(q1*x)+c2*exp(q2*x)+c3*exp(q3*x)

    where c1, c2 and c3 are (complex) constant that can be fixed by initial conditions and
    q1=1
    q2=(-1+i*sqrt(3))/2
    q3=(-1-i*sqrt(3))/2

    This can be re-written in the real field as

    y(x)=exp(x)* c1 + A*exp(-x/2)*cos(sqrt(3)*x+B) )

    where A and B are new constants depending on c2 and c3 only.
     
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