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Homework Help: 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


    2. Relevant equations


    3. The attempt at a solution


    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


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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:


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


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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]




  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


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