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

1. Feb 26, 2009

Jack_O

1. The problem statement, all variables and given/known data

2. Relevant equations

N/A

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. Feb 26, 2009

djeitnstine

The answer to your auxiliary equation is wrong, m=+/- 2i not +/- 2 so the homogeneous solution is of the form $$x_{h}=C_{1}cos(2t)+C_{2}Sin(2t)$$

3. Feb 26, 2009

Jack_O

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)]

4. Feb 26, 2009

djeitnstine

make your solution without complex coefficients so $$y_{h}=C_{1}sin2t+C_{2}cos2t$$

then work out the result $$C_{1}sin0+C_{2}cos0=1$$
$$C_{2}=1$$

$$y_{h}'=2C_{1}cos2t-2C_{2}sin2t$$

$$2C_{1}cos0-2C_{2}0=-2$$

$$-2C_{1}-2=-2$$

$$C_{1}=0$$....

5. Feb 26, 2009

Jack_O

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.

6. Feb 26, 2009