Question

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)

Answer 1

We solve the given system of differential equations by using elimination method.