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# How do you solve a pair of coupled differential equations where the matrix of coeffs has complex Eigenvalues?

I'm trying to solve the coupled differential equations: dx/dt=x+4y and dy/dt=-5x+5y, but if you put the coefficients of x and y into a matrix, it gives complex Eigenvalues. So how do I solve the equations? Thanks for your help.

### 2 Answers

- melvinaLv 44 years ago
I doubt very lots that a closed form answer exists. it would, yet i may well be bowled over. in spite of the undeniable fact that it lends itself fantastically for numerical fixing. a million) y' is often +ve so the function is rarely reducing 2) as x --> ±?, y' --> 0 So y(x) might seem resembling the erf(x) function. *** nicely certainly i think of the respond is y(x) = 0 identically. If y'(0) = 0, then y never gets around to shifting from y(0) = 0. **** For different preliminary circumstances, y(x) will resemble the errors function, in spite of the undeniable fact that that's going to be contained between consecutive values n?. that's because of the fact on each and every occasion y = n?, y' = 0, and for that reason y=n? will continuously be an aymptote to the function.