Solve the given system of differential equations by systematic
elimination.
(D2 − 1)x
−
y
=
0
(D − 1)x
+
Dy
=
0
I had this as my answer and webassign rejected it:
(x(t), y(t)) = c_1e^t+e^{-\left(\frac{t}{2}\right)}\left(c_2\cos
\left(\frac{\sqrt{3}}{2}t\right)+c_3\sin
\left(\frac{\sqrt{3}}{2}t\right)\right),e^{-\left(\frac{t}{2}\right)}\left(\left(-\frac{3}{2}c_2-\frac{3\sqrt{3}.}{4}c_3\right)\cos
\left(\frac{\sqrt{3}}{2}t\right)+\left(\frac{-3}{2}c_3+\frac{3\sqrt{3}}{4}c_2\right)\sin
\left(\frac{\sqrt{3}}{2}t\right)\right)