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Finding the particular solution to an ODE with set boundary conditions.

  1. Feb 26, 2009 #1
    1. The problem statement, all variables and given/known data

    80234296.jpg

    2. Relevant equations

    N/A

    3. The attempt at a solution

    5184b1eb.jpg

    The problem and attempt are as above, i'm not sure where to go from here though. I'm not sure what to do with the boundary condition of dx/dt=-2 and t=0.
    Any help appreciated.
     
  2. jcsd
  3. Feb 26, 2009 #2

    djeitnstine

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    The answer to your auxiliary equation is wrong, m=+/- 2i not +/- 2 so the homogeneous solution is of the form [tex]x_{h}=C_{1}cos(2t)+C_{2}Sin(2t)[/tex]
     
  4. Feb 26, 2009 #3
    Thanks for pointing that out, i've had another go and realised i needed to differentiate the general solution and then sub in the other boundaries to get the other simultaneous equation. My completed solution looks like this:

    742403f1.jpg

    I have also done part c), got the answer x=(i/sqrt3)[-e^(2it)+e^(-2it)]
     
  5. Feb 26, 2009 #4

    djeitnstine

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    make your solution without complex coefficients so [tex]y_{h}=C_{1}sin2t+C_{2}cos2t[/tex]

    then work out the result [tex]C_{1}sin0+C_{2}cos0=1[/tex]
    [tex]C_{2}=1[/tex]

    [tex]y_{h}'=2C_{1}cos2t-2C_{2}sin2t[/tex]

    [tex]2C_{1}cos0-2C_{2}0=-2[/tex]

    [tex]-2C_{1}-2=-2[/tex]

    [tex]C_{1}=0[/tex]....
     
  6. Feb 26, 2009 #5
    If i use Euler's formula to sub out e^(2it) for cos(2t)+i*sin(2t) won't i still be left with complex coefficients? Their are complex numbers in the (1+i) term. I don't see how i can cancel out all the complex numbers.
     
  7. Feb 26, 2009 #6

    djeitnstine

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