 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2009/differential-equations/8/i/solution

The principal matrix is

(a b b c)

. The equation is elliptic at a point when

b^{2} - a c < 0

, equivalently the principal form has eigenvalues of the same nonzero sign and no real characteristic directions.

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