Find the real solution of the system
The solution is
Continuous dynamical system with eigenvalues
Consider the linear system where A is a real matrix with complex eigenvalues (and ).
Consider an eigenvector role="math" localid="1659877431239" with eigenvalue .
Then where . Recall that is the coordinate vector of with respect to basis .
Consider the given system as follows.
No, to find the eigenvalues of the coefficient matrix as follows.
Simplify further as follows
Therefore, the eigenvalues are and
To find a formula for trajectory as follows.
Therefore, the eigenvectors are as follows.
Then by the theorem, the general solution for the system is as follows.
Similarly, the values of p, q and S are as follows.
Substitute the value 0 for p and 6 for q and for S in as follows.
Hence, the solution for the system is
where x and y are arbitrary constants.
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