MATH307 April 2006
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Question 02 (b)
Consider the diagonalizable matrix
(b) Find the solution of the differential equation satisfying the initial condition .
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The solution for a differential equation of the form and A is 2 by 2 and diagonalizable has the form
where are the eigenvalues of A and are their respective eigenvectors.
can be obtained by plugging in the initial condition
Solving should give you
therefore the solution is