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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Special Forms There are a number of nice special forms of some polynomials which can make factoring easier for us on occasion. Following are the special forms. a 2 + 2ab +
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Build a Fine Automaton which accept all words which have different first and last letters (that is if the word starts with an "a" to be accepted it should end with "b" and vice ver
how to get the answer
Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations. In this case we need soluti
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