I cannot solve the following first order system of differential equations. I´ve calculated the eigenvalues (λ1 = 1 + i, λ2 = 1 - i) and the eigenvectors E1 = [1, i] , E2 = [i , 1] (column vectors). But, I cannot found a fundamental set of real solutions.

Question

I cannot solve the following first order system of differential equations. I´ve calculated the eigenvalues  (λ1 = 1 + i,  λ2 = 1 - i) and the eigenvectors E1 = [1, i] , E2 = [i , 1]  (column vectors). But, I cannot found a fundamental set of real solutions.

anonymous · Answer

$$dx/dt = x - y $$$$dy/dt = x + y$$
(System of differential equations)

anonymous · Answer

$$X (t) =\left(\begin{matrix}1 \ i\end{matrix}\right)e ^{(1+i)t} + \left(\begin{matrix}i \ 1\end{matrix}\right)e ^{(1-i)t}$$ 

That is the solution, where X(t) is...$$X(t) = \left(\begin{matrix}x(t) \ y(t)\end{matrix}\right)$$

Well, ¿Someone knows how to rewrite  it into a set of only real solutions? Please write the steps...

anonymous · Answer

@mahmit2012 plzzzz help mee http://openstudy.com/study?signup#/updates/4ff05fd6e4b0389b6ee03cd2

anonymous · Answer

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