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(Solved): We wish to solve the system vec(x)^(')=[[2,-1],[0,1]]vec(x)+[[sin(t)],[e^(t)]] via eigenvector decom ...
We wish to solve the system
vec(x)^(')=[[2,-1],[0,1]]vec(x)+[[sin(t)],[e^(t)]]
via eigenvector decomposition.
Let vec(v)_(1) be an eigenvector for the smaller eigenvalue of the coefficient matrix and vec(v)_(2) be an eigenvector for the larger eigenvalue. Let us pick the
eigenvectors such that vec(v)_(1)=[[-1],[?]] and vec(v)_(2)=[[-1],[?]]. What are these eigenvectors:
Then fill in the equation to write it in the eigenvector decomposed form.
vec(v)_(1)\xi _(1)^(')+vec(v)_(2)\xi _(2)^(')=,vec(v)_(1)\xi _(1)+,vec(v)_(2)\xi _(2)+vec(v)_(1)+vec(v)_(2)