I am trying to find an exact solution from this general solution,
X=$2\cos(-t+c+\frac{1}{16} \epsilon^2 t)-\frac{\epsilon}{4}\sin(-3t+3c+\frac{3}{16}\epsilon^2 t)$
with initial conditions $x(0)=A$ and $\dot x(0)=B.$
Here, c is unknown and $\epsilon$, A and B are known parameters.
So, I get two equations as follows:
$x(0)=2\cos(c)-\frac{\epsilon}{4}\sin(3c)=A$
and
$\dot x(0)=-2\sin(c)(\frac{\epsilon^2}{16}-1)-\frac{\epsilon}{4}\cos(3c)(-3+3\frac{\epsilon^2}{16})=B$
But I don't know how to get an expression for c using these two equations.