The coefficient matrix for a system of linear differential equations of the form y^1=Ay has the given eigenvalues and eigenspace bases. Find the gener

Tolnaio 2021-01-23 Answered
The coefficient matrix for a system of linear differential equations of the form y1=Ay
has the given eigenvalues and eigenspace bases. Find the general solution for the system
λ1=2i{[1+i2i]},λ2=2i{[1i2+i]}
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dessinemoie
Answered 2021-01-24 Author has 90 answers
By theorem 6.19 we know that the solution is
y=c1eλ1tu1++cneλntun
with λi the eigenvalues of the matrix A nad ui the eigenvectors Thus for this case we then obtain the general solution:
[y1y2]=y=c1e2it[1+i2i]+c2e2it[1i2+i]
Thus we obtain:
y1=c1(cos(2t)sin(2t))+c2(cos(2t)+sin(2t))
y2=c1(2cos(2t)+sin(2t))+c2(cos(2t)2sin(2t))
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