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

  • Thread starter Jack_O
  • Start date
65
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1. Homework Statement

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2. Homework 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.
 

djeitnstine

Gold Member
614
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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]
 
65
0
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)]
 

djeitnstine

Gold Member
614
0
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]....
 
65
0
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.
 

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