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Aug24-08, 06:07 PM
Other Sci
Sci Advisor
P: 1,393
You forgot the constant in the solution to the homogeneous equation:
XH = Aet

Therefore the general solution to the non-homogeneous ODE is:
x(t) = Aet + (1/2)(sin(t)-cos(t))

To find the value for A, you should use the boundary condition x(0) = x0. (You should find that A = x0 + 1/2).

Alternatively, you could carry the constant through your original solution and solve for C using the boundary condition.