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

CMIIh 2021-09-20 Answered
The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
λ1=1{21},λ2=3{31}
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tafzijdeq
Answered 2021-09-21 Author has 92 answers

By theorem 6.19 we know that the solution is y=c1(eλ1t)u1+...+cn(eλnt)un

wiht λi the eigenvalues of the matrix A and ui, the eigenvalues.

Thus for this case we then obtain the general solution:

[y1,y2]=y=c1et[2,1]+c2e3t[3,1]

Thus we obtain:

y1=2c1et+3c2e3t

y2=c1et+c2e3t

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