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Solve the given system of differential equations by systematic elimination. (D2 − 1)x − y = 0 (D − 1)x + Dy = 0 I had this...

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Basic Math

Solve the given system of differential equations by systematicelimination.

(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)


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